Derivatives Final

Make Your Future With Options

FUTURES – THE CONCEPTA futures contract can be defined as a standardized agreement between the buyer and the

seller in terms of which the seller is obligated to deliver a specified asset to the buyer on a specified date and the buyer is obligated to pay to the seller the then prevailing futures price in exchange of the delivery of the asset.

The futures contracts represent an improvement in the forward contract in terms of standardization, performance guarantee and liquidity. Whereas forward contracts are not standardized, the futures contract are standardized ones, so that1. The quantity of the commodity or the other asset which could be transferred or would form the basis of gain/loss on maturity of the contract,2. The quality of the commodity – if a certain commodity is involved – and the place where delivery of the commodity would be made,3. The date and month of delivery,4. The units of price quotation,5. The minimum amount by which the price would change and the price limits of the day’s operations, and other relevant details are all specified in a futures contract.

Thus, in a way, it becomes a standard asset, like any other asset to be traded.

Futures contracts are traded on commodity exchanges or on other futures exchanges. People can buy of sell futures like other commodities. When an investor buys a futures contract (so that he takes a long position) on an organized futures exchange, he is, in fact, assuming the right and obligation of taking delivery of the specified underlying item (say 10 quintals of wheat of a specified grade) on a specified date. Similarly, when an investor sells a contract, to take a short position, one assumes the right and obligation to make delivery of the underlying asset. While there is a risk of non-performance of a forward contract, it is not so in case of a futures contract. This is because of the existence of a clearing house or clearing corporation associated with the futures exchange, which plays a pivotal role in the trading of futures. Unlike a forward contract, it is not necessary to hold on to a futures contract until maturity – one can easily close out a position in the futures contract. Something.

RELATIONSHIP BETWEEN SPOT AND FUTURES PRICEThe price of a commodity (here we are not restricting ourselves to equity stock as the

underlying asset) is, among other things, a function of: Demand and supply position of the commodity Storability – depending on whether the commodity is perishable or not Seasonality of the commodity

To understand the linkage between spot and futures price, let us consider an example. Example

If John is certain that the demand-supply position of wheat is such that 3 months from now, the price of wheat is likely to go up, he should be tempted to buy wheat now and sell the stock after 3 months at a higher price. For this purpose, he will hire a godown, stock the inventory, pay interest on the money invested I the stock as well as pay incidental charges in holding the inventory, like, handling charges, insurance charges, etc., collectively called the ‘carrying costs’. Let us assume that he buys a unit of wheat at Rs. 100 and the carrying costs aggregates Rs. 6 per unit. Logically, to earn profit, he would have to be sure that spot price of wheat; 3 months from now should be more than Rs. 106. Now if others also have the same information that the wheat prices are likely to go up beyond the carrying cost, the number of buyers would increase. As the current demand for wheat increases because of this information, the current spot price also starts climbing. The current

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spot price would keep on increasing till the anticipated future spot price becomes equal to current spot price plus the carrying costs.

As we have already seen, the future spot price tends to equal the current spot price plus the carrying costs. Suppose the current spot price is Rs. 100 and the carrying costs are Rs. 6. the predicted futures price, say, 3 months from now is Rs. 110. There would be a tendency for the current spot price to rise from Rs. 100 to Rs. 104, as any increase beyond this level would mean a loss in the transaction.

Thus, the current spot price would tend towards a level where there is no profit or no loss situation for both the buyer and seller alike. The conclusion, therefore, is that in a perfectly predictable and certain market, neither the buyer nor the seller would be interested in futures trading. If, future spot prices could be forecast with 100% certainty, the very idea of futures market would vanish. As a corollary, we can say that it is the element of uncertainty, which gives rise to a futures market.

BASISThe difference between the prevailing spot price of an asset and the futures price is known as

the basis, i.e.Basis = Spot price – Futures price

In a normal market, the spot price is less than the futures price (which includes the full cost-of-carry) and accordingly the basis would be negative. Such a market, in which the basis decided solely by the cost-of-carry, is known as the Contango Market.

Basis can become positive, i.e. the spot price can exceed the futures price only if there are factors other than the cost-of-carry to influence the futures price. In case this happens, then basis become positive and the market under such circumstances is termed as a Backwardation Market or Inverted Market.

Basis will approach zero towards the expiry of the contract, i.e. the spot and futures prices converge as the date of expiry of the contract approaches. The process of the basis approaching zero is called Convergence.

As already explained above, the relationship between futures price and cash price is determined by the cost-of-carry. However, there might be factors other than cost-of-carry, especially in case of financial futures I which there may be carry returns like dividends, in addition to carrying costs, which may influence this relationship.

The cost-of-carry model in financial futures, thus, is Futures price = Spot price + Carrying costs – Returns (dividends, etc.)

Example

The price of ACC stocks on 31st December 2000 was Rs. 220 and the futures price on the same stock on the same date, for March 2001 was Rs. 230. Other features of the contract and related information are as follows:Time of expiration - 3 months (0.25 year)Borrowing rate - 15% p.a.Annual Dividend on the stock - 25% payable before 31.03.2001Face value of the stock - Rs. 10

Based on the above information, the futures price for ACC stock on 31st December 2000 should be:

= 220 + (220 x 0.15 x 0.25) – (0.25 x 10)= Rs. 225.75

Thus, as per the ‘cost of carry’ criteria, the futures price is Rs. 225.75, which is less than the actual price of Rs. 230 in February 2001. This would give rise to arbitrage opportunities and consequently the two prices will tend to converge.

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Valuation of futures

Let us take a simple example of a fixed deposit in a bank. Rs. 100 deposited in the bank at a rate of interest of 10% would become Rs. 110 after 1 yr. Based on annual compounding; the amount will become Rs. 121 after 2 yrs. Thus, we can say that the forward price of the fixed deposit of Rs. 100 is Rs. 110 after 1 yr. and Rs. 121 after 2 yrs.

As against the usual annual, semi-annual and quarterly compounding, continuous compounding are used in derivative securities. In terms of annual compounding, the forward price can be computed through the following formula:A = P (1 + r / 100)t Where A is the terminal value of an amount P invested at the rate of interest of r % p.a. for t years.

Now, if compounding was done twice a year, the amount at the end of 2 years can be calculated as follows:

Beginning of period Principle Interest Amt. at the end

I Half–year 1000 1000 x 0.05 = 50 1050II Half-year 1050 1050 x 0.05 = 52.50 1102.50III Half-year 1102.50 1102.5 x 0.05 = 55.125 1157.6254IV Half-year 1157.625 1157.625 x 0.05 = 57.881 1215.51

It is observed that with all the inputs being the same, the amount is a little higher when the frequency of compounding is increased from one to two in each year. With the still greater compounding frequency, the amount at the end of the 2 yr period would increase. For instance, for different compounding period at the end of 2 yrs are given below:

Compounding Amount (Rs.)Quarterly 1218.40Monthly 1220.39Weekly 1221.17Daily 1221.37

In general terms,A = P (1 + r / m) m n

where r is the per annum rate of interest, m is the number of compounding per annum and n is the number of yrs. For quarterly compounding, for eg. m = 4, while for daily compounding, m = 365.

To carry the idea further, if the number of compounding per annum increases more and more, the time period between successive compounding would steadily fall. In the extreme case, the compounding may be thought to be continuous. In such an event, it can be shown mathematically that the amount may be calculated as follows:A = Pen r

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t

Make Your Future With OptionsWhere all symbols carry the same meaning as before, and e is a mathematical constant whose value is 2.7183. Since the compounding is continuous, the amount is likely to be the largest. To know the exact amount, we make the following calculation:A = 1000 x 2.71832 x 0.1

= 1000 x 1.22140 = Rs. 1221.40

In case there is a cash income accruing to the security like dividends, the above formula will read as follows:A = (P – I) em r

Where I is the present value of the income flow during the tenure of the contract.Example

Consider a 4 month forward contract on 500 shares with each share priced at Rs. 75. Dividend @ Rs. 2.50 per share is expected to accrue to the shares in a period of 3 months. The CCRRI is 10% p.a. the value of the forward contract is as follows:Dividend proceeds = 500 x 2.50 = 1250Present value of Dividend = 1250e- (3/12) (0.10)

= 1219.13Value of forward contract = (500 x 75 – 1219.13) e(4/12) (0.10)

= 36280.87 x e0.033

= Rs. 37498.11

Future’s market

As in any other trade, the futures trade has to have a market to facilitate buying and selling. As the futures markets involve the operation and execution of financial deals of an enormous magnitude, their efficiency has to be of the highest quantity. Not only the size of the monetary operation that a futures market handles but also the critical significance it has on the equilibrium of the commodities / stocks is what makes the operation of the market so crucial.

PURPOSE OF A FUTURES MARKETFutures markets provide flexibility to an otherwise rigid spot market because of their very

concept, which allows a wholistic approach to the price mechanism involved in futures contracts. The future price of a commodity is a function of various commodities related and market related factors and their inter-play determines the existence of a futures contract and its price. Futures markets are relevant because of various reasons, some of which are as follows:

1. Quick and Low Cost Transactions:Futures contracts can be created quickly at low cost to facilitate exchange of money for goods to be delivered at future date. Since these low cost instruments lead to a specified delivery of goods at a specified price on a specified date, it becomes easy for the finance managers to take optimal decisions in regard to protection, consumption and inventory. The costs involved in entering into futures contracts is insignificant as compared to the value of commodities being traded underlying these contracts.

2. Price Discovery Function:The pricing of futures contracts in corporates a set of information based on which the producers and the consumers can get a fair idea of the future demand and supply position of the commodity and consequently the future spot price. This is known as the ‘price discovery’ function of future.

3. Advantage to Informed Individuals:Individuals who have superior information in regard to factors like commodity demand-supply, market behaviour, technology changes, etc., can operate in a futures markets and impart efficiency

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Make Your Future With Optionsto the commodity’s price determination process. This, in turn, leads to a more efficient allocation of resources.

4. Hedging Advantage:Adverse price changes, which may lead to losses, can be adequately and efficiently hedged against through futures contract. An individual who is exposed to the risk of an adverse price change while holding a position, either long or short a commodity, will need to enter into a transaction which could protect him in the event of such an adverse change. For eg, a trader who has imported a consignment of copper and the shipment is to reach within a fortnight may sell copper futures if he foresees fall in copper prices. In case copper prices actually fall, the trader will lose on sale of copper but will recoup through futures. On the contrary if prices rise, the trader will honour the delivery of the futures contract through the imported copper stocks already available with him.

Thus, futures markets provide economic as well as social benefits. Through their functions of risk mgt. and price discovery.

TYPES OF ORDERS Market Order

When a trader places a buy or sells order at a price, which prevails in the futures pit at the time, the order is given; it is called a Market Order.Limit Order

If the trader specifies a particular price or the price limit within which the order should be executed, such an order is called a Limit Order. In such orders, the inherent risk is that the specified price or the band may never be hit during the day and the position may not be closed out.Market-If-Touched (MIT) Order

If an order is executed at the best available price after trade occurs at a particular price or at a price more favourable then the specified price, it is called the Market-if-Touched Order.Stop Loss Order

When a trader holds a position, either long or short and wants to restrict his downsize, he would place an order specifying a rate at which the deal could close out. This would insure him against a run away loss in the event of a drastic adverse price movement. Stop Loss Orders are normally placed by specifying a range in which the order should be executed instead of giving a single price order. The risk in the latter case is that the order may not get executed as in a violent price movement; the specified price may get jumped.

Good Till Cancelled (GTC) OrderIn terms of National Stock Exchange (NSE) regulations good till cancelled orders shall be

cancelled at the end of 7 calendar days from the date of entering the order.

THE CLEARING MECHANISM A clearing house is an inseparable part of a futures exchange. This exchange acts as a seller for

the buyer and a buyer for the seller in the process of execution of a futures contract. For example, the moment the buyer and the seller agree to enter into a contract, the clearing

house steps in and bifurcates the transaction, such that, Buyer buys from the clearing house, and Seller sells to the clearing house.

Thus, the buyer and the seller do not get into the contract directly; in other words, there is no counter party risk. The idea is to secure the interest of both. In order to achieve this, the clearing house has to be solvent enough. This solvency is achieved through imposing on its members, cash margins and/or bank guarantees or other collaterals, which are encashable fast. The clearing house monitors the solvency of its members by specifying solvency norms.

The solvency requirements normally imposed by the clearing house on their members are broadly as follows.1. Capital Adequacy

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Make Your Future With OptionsCapital adequacy norms are imposed on the clearing members to ensure that only financially sound firms could become members. The extent of capital adequacy has to be market specific and would vary accordingly.2. Net Position LimitsSuch limits are imposed to contain the exposure threshold of each member. The sum total of these limits, in effect, is the exposure limit of the clearing association as a whole and the net position limits are meant to diversify the association’s risk.

3. Daily Price LimitsThese limits set up the upper and the lower limits for the futures price on a particular day and incase these limits are touched the trading in those futures is stopped for the day.

4. Customer MarginsIn order to avoid unhealthy competition among clearing members in reducing margins to attract customers, a mandatory minimum margin is obtained by the members from the customers. Such a step insures the market against serious liquidity crisis arising out of possible defaults by the clearing members owing to insufficient margin retention.

In order to secure their own interest as well as that of the entire system responsible for the smooth functioning of the market, comprising the stock exchanges, clearing houses and the banks involved, the members collect margins from their clients as may be stipulated by the stock exchanges from time to time. The members pass on the margins to the clearing house on the net basis i.e. at a stipulated percentage of the net purchases and sale position while they collect the margins from clients on gross basis, i.e. separately on purchases and sales.The stock exchanges impose margins as follows:a) Initial margins on both the buyer as well as the seller.b) Daily maintenance margins on both.c) The accounts of the buyer and the seller are marked to the market daily.

MARGINSThe concept of margin here is the same as that for any other trade, i.e. to introduce a financial

stake of the client, to ensure performance of the contract and to cover day to day adverse fluctuations in the prices of the securities bought. The margin paid by the investor is kept at the disposal of the clearing house through the brokerage firms. The clearing house gets the protection against po0ssible business risks through the margins placed with it in this manner and by the process of ‘marking to market’ (it means, debiting or crediting the clients’ equity accounts with the loss or gains of the day, based on which, margins are sought or released).The margin for futures contract has two components Initial margin, and Maintenance margin.

Initial MarginUnlike in an options contract where only the buyer is obligated to perform and not the seller

(writer), in a futures contract both the buyer and the seller are required to perform the contract. Accordingly, both the buyer and the seller are required to put in the initial margins. The initial margin is also known as the performance margin and is usually 5 to 155 of the purchase price of the contract. The margin is set by the stock exchange keeping in view the volume of business and the size of transactions a well as operative risks of the market in general.

The initial margin is the first line of defense for the clearing house. This protection is further reinforced by prescribing maintenance margin.

Maintenance Margin

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Make Your Future With OptionsIn order to start dealings with a brokerage firm for buying and selling futures, the first

requirement for the investor is to open an account with the firm. This account, called the equity account, has to be kept separate from any other account including the margin accounts. Maintenance margin is the margin required to be kept by the investor in the equity account equal to or more than a specified percentage of the amount kept as initial margin. Normally, the deposit in the equity account is equal to or more than 75% to 80% of the initial margin.

In case this requirement is not met, the investor is advised to deposit cash to make up the shortfall. If the investor does not respond, then the broker will close out the investor’s position by entering a reversing trade in the investor’s account.

ExampleA buyer buys a futures contract @ Rs. 50 per share for 500 shares from a seller. Both make a

deposit of Rs. 2,500, being 10% of the total investment of Rs. 25.000 towards the initial margin. The next day, the stock price rises to Rs. 52 per share. The equity of the buyer increases to Rs.

3,500 and that of the seller decreases to Rs. 1,500. As the maintenance margin is required to be maintained at 80% of the initial margin, the buyer and the seller are required to have a minimum equity of Rs. 2,00 everyday. The buyer has a surplus of Rs. 1,500 and he has the liberty of withdrawing this sum. The seller, on the other hand, is short of Rs. 500 and would be called upon to make up the shortfall by depositing cash. However, if the seller is unable to pay, the broker would enter a reversing trade by purchasing a future of the same expiration.

Other future contractSTOCK INDEX FUTURES

Stock index futures are drawn on stock market indices and each of these contracts are characterized by payment of cash on the delivery date of an amount equal to a multiplier times the difference between:a) The value of the index at the close of the last trading day of the contract, andb) The purchase price of the futures contract. INTEREST RATES FUTURES

Futures written on fixed income instruments as the underlying securities are known as interest rate futures. Predetermined periodical income through the life of such instruments and principle maturity amount at the end of the instrument’s life are the usually the features of such securities. These instruments have become an integral part of all balance portfolios and accordingly the growth of these securities has grown substantially. But ever since, interest rates on fixed income instruments have become highly volatile, the need for suitable hedge against this volatility has risen. Thus, two prime-movers for the growth of interest rate futures are:1. the tremendous growth in the fixed income securities, and2. increased volatility in the interest rates in the market.

In order to hedge against the risks arising as a result of these two factors, interest rate futures come in handy apart from other hedging instruments like interest-rates swaps. Interest rate futures can be used to hedge against interest rate risk and to crystallize future investment yields or future cost of borrowing.

WHAT IS AN OPTION?

Option is a legal contract in which the writer of the contract grants to the buyer, the right to purchase from or to sell to the writer a designated instrument or a scrip at a specified price within a specified period of time.

The right to purchase a specified stock is called the call option, while the right to sell a specified stock is called a put option.

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ExampleSuppose a writer of an option writes a contract, which conveys or grants to the buyer the right

to bur 100 shares of ITC from him, i.e. from the writer at the rate of Rs. 650 per share. This option is called a call option and is designated as 100 ITC 650 call.

Similarly, if a writer writes an option which grants to the buyer the right to sell to the writer 100 shares of ITC at Rs. 650 per share, such an option is called a put option and is designated as 100 ITC 650 put.

It should be noted that in a call option transaction, there is not put option involved. The writer is writing or selling a call option and the buyer is buying a call option. Similarly, in the case of a put option transaction there is no call option involved. The writer is writing or selling a put option and the buyer is buying a put option.

WHO CAN WRITE AN OPTION?Anyone eligible to enter into contract as per the Law of Contract can write an option irrespective

of the fact whether one owns the underlying stock or not.If the writer of a call option owns the stock that he is obliged to deliver upon exercise of the call

he has written, he is called a covered call writer.On the other, if the writer of the call option does not own the stock he has written the option for,

he is called an uncovered or naked call writer and the option is called an uncovered or naked call option.

OBLIGATION OF THE OPTION WRITER AND BUYERThe writer is legally obligated to perform according to the terms of the option. On the other

hand, the buyer of the option has bought a write to exercise the option and is under no obligation to exercise the option. He can conveniently let the option lapse on the date of expiration of the option.

The significance of this feature of an option is explained through the following example.

ExampleSuppose you buy a 100 ITC 650 Call option contract. During the expiration period, the stock

price does not appreciate enough to cover even the premium paid, i.e., you do not gain anything by exercising the option. The options contract confers on you the right to either invoke the contract or let it lapse. Invoking the contract means – calling upon the writer to deliver the stock at the contract price. This would be futile as this stock is available at equal to or even less than the exercise price in the market. By letting the option lapse the buyer gets out of the contract, as he is not obligated to perform. However, the writer or the seller is under the obligation to perform right up to the expiry of the contract whenever called upon buy the buyer of the option to do so.

ESSENTIAL INGREDIENTS OF AN OPTION CONTRACTAn options contract has four essential ingredients:1. The name of the company on whose stock the option contract has been derived.2. The quantity of the stock required to be delivered in the case of exercise of the option.3. The price, at which the stock would be delivered, or the exercise price or the strike price.4. The date when the contract expires, called the expiration date.

CALL OPTIONSA call option gives the buyer the right to purchase a specified number of shares of a particular

company from the option writer (seller) at a specified price (called the exercise price) up to the

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Make Your Future With Optionsexpiry of the option. In other words, the option buyer gets a right to call upon the option seller to deliver the contracted shares any time up to the expiry of the option. The contract, thus, is only one-way obligation, i.e. the seller is obligated to deliver the contracted shares while the buyer has the choice to exercise the option or let the contract lapse. The buyer is not obligated to perform.

Position Graphs

An option buyer starts with a loss equivalent to the premium paid. He has to carry on with the loss till the stock's market price equals the exercise price as shown in (a). The intrinsic value of the option up to this point remains zero and thus, runs along the X-axis. As the stock price increases further, the loss starts reducing and gets wiped out as soon as the increase equals the premium, represented on the graph by point ‘b’, also called the break even point. The profitability line starts climbing up at an inclination of 45 degrees after crossing the X-axis at ‘b’ and from thereon moves into the positive side of the graph. The inclined line beyond the point ‘b’ indicates that the option acquires intrinsic value and is, thus referred to as the intrinsic value line.

The position graph in (b) represents the profitability status of the writer who does not own the stock, i.e., a naked or an uncovered writer. The graph is logically the inverse of that for the option buyer.

RATIONALE OF BUYING CALL OPTIONSThere are broadly three reasons why an investor could buy a call option instead of buying the

stock outright. These are as follows:

1. Return on InvestmentAn investor anticipates that a stock is shortly going to appreciate from Rs. 300 to Rs. 400 per share and buying 100 shares of the stock would involve an investment of Rs. 30,000. However, a call option on the stock is available at a premium of Rs. 20. Let us assume that the stock's share actually goes up to Rs. 400 within the currency of the option. The investor thus makes a profit of Rs. 80 per share (400 (300+20)]. His investment was only to the extent of premium paid, i.e. Rs. 20 per share. Thus, the investor got an appreciation of 400% on his investment. Had he bought the stock outright, the investor would have made Rs. 100 per share on an investment of Rs. 300, i.e. 33%. This should be sufficient motivation for the investor to go in f6r call options on the stock as against outright buying of the stock.

2. HedgingTrading with the objective of reducing or controlling risk is called HEDGING. An investor, having short sold a stock, can protect himself by buying a call option. In the event of an increase in the stock's price, he would at least have the commitment of the option writer to deliver the stock at the exercise price, whenever he is to effect delivery for the stock, sold short. The maximum loss the

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Make Your Future With Optionsinvestor may be exposed to would be limited to the premium paid on the call option. Options can thus be used as a handy tool for hedging.

3. ArbitrageArbitrage involves buying at a lower price and selling- at a higher price, if it so exists. As in any other trade, options arbitrage provides an opportunity to earn money by exploiting the pricing inefficiencies, which may exist within a market or between two markets or two products and as a result tends to bring perfection to the market.

PUT OPTIONA put option gives a buyer the right to sell a specified number of shares of a particular stock to

the option writer at a specified price (called the exercise price) any time during the currency of the option.

Position Graphs

RATIONALE OF BUYING A PUT OPTIONAn investor, if he anticipates fall in the price of some stock, has the following alternatives:1. Sell the stock short, i.e. enter a sales transaction without owning the stock. In the event of a fall in the stock price, he can buy the stock at a lower price and can deliver the stock sold to the buyer, thus making profit equal to the fall in the price. However, in case the stock price appreciates instead of declining, the investor would be exposed to unlimited loss.

2. Write a call option without owning the stock, i.e. writing a naked call option. Writing such an option is similar to selling short, the only difference being that the loss in the event of appreciation in the stock price would be curtailed to the extent of the premium received on writing the call option, which may not be sufficient attraction.3. Purchase a put option. The purchase of a put option is the most desirable policy as compared to either going short or writing a naked call option. The first reason is that the investment in buying a put option is restricted to the premium as against a larger sum required for going short. Thus, as in the case of a call option, the return on investment on buying a put option is much higher as compared to going short on the stock.

Secondly, in the event of increase in the stock price, the loss to the put option buyer is restricted to the premium paid. Option Type Buyer of Call (Long

Position)Writer of Call(Short Position)

Call Right to buy asset Obligation to sell assetPut Right to sell asset Obligation to buy asset

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AMERICAN v/s EUROPEAN OPTIONSThe definitions of options, both call and put, given above apply to the American-style options. An

American option can be exercised by its owner at any time on or before the expiration date. Besides the American type there are European-style options as well. In case of European options, the owner can exercise his right only on the expiration date and not before it. It may be pointed out however, that most of the options traded in the world, including those in Europe, are of the American style.

Terminology’s

Before into the concepts and mechanics of options trading, we need to be familiar with the basic terminology as they are repeatedly used in case of options and also the factors that influence the option price.

EXERCISE PRICE The exercise price (also called the strike price) is the price at which the buyer of a call option can purchase the stock during the life of the option, or the buyer of the put option can sell during the life of the option.

Exercise price is that price at which the writer has to deliver the stock to the call option buyer and buy from the put buyer irrespective of the prevailing market price in case the latter decides to exercise the option.

EXPIRATION DATEExpiration Date is the date on which the option contract expires, i.e. the last date on which

options contract can be exercised.Options usually have either a monthly and/or quarterly expiration cycle. The maturity period for an option does not normally exceed nine months.

PREMIUMPremium is the price that the buyer of an option, whether call or put, pays to the writer of the

option, for the rights conveyed by the option. The premium of the option is a function of variables, such as: Current stock price, Strike price, Time to expiration, Volatility of stock, and Interest rates.

The buyer pays the premium to the seller, which belongs to the seller whether the option is exercised, or not. If the owner of an option decided not to exercise the option, the option expires and becomes worthless. The premium becomes the profit of the option writer, while if the option is exercised; the premium gets adjusted against the loss that the writer incurs upon such exercise.

IN-THE-MONEYA call option is In-the-Money if the prevailing stock price (of the underlying asset) is greater than

the exercise price.

AT-THE-MONEY

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Make Your Future With OptionsIn case the call’s market price is the same as its exercise price, it would bee called at-the-money

or at-the-market.

OUT-OF-THE-MONEYSimilarly, if the market price of the stock is less than the exercise price, it shall be called out-of-

the-money.

These concepts are tabulated below, wherein S indicates the present value of the stock and E is the exercise price.

Condition Call Option Put OptionS > E In-the-Money Out-of-the-MoneyS < E Out-of-the-Money In-the-MoneyS = E At-the-Money At- the-Money

INTRINSIC VALUE The premium or the price of an option is made up of two components, namely, intrinsic value

and time value. Intrinsic value is termed as parity value.For an option, the intrinsic value refers to the amount by which it is in money if it is in-the-

money. Therefore, an option, which is out-of-the-money or at-the-money, has zero intrinsic value.For a call option, which is in-the-money, then, the intrinsic value is the excess of stock price (S)

over the exercise price (E), while it is zero if the option is other than in-the-money. Symbolically, Intrinsic Value of a call option = max (0, S – E)

In case, of an in-the-money put option, however, the intrinsic value is the amount by which the exercise price exceeds the stock price, and zero otherwise. Thus, Intrinsic Value of a put option = max (0, E - S)TIME VALUE

Time value is also termed as premium over parity. The time value of an option is the difference between the premium of the option and the intrinsic value of the option. For, a call or a put option, which is at-the-money or out-of-the-money, the entire premium about is the time value. For an in-the-money option time value may or may not exist. In case, of a call which is in-the-money, the time value exists if the call price, C, is greater than the intrinsic value, S – E. Generally, other things being equal, the longer the time of a call to maturity, the greater will be the time value.

This is also true for the put options. An in-the-money put option has a time value if its premium exceeds the intrinsic value, E – S. Like for call options, put options, which are at-the-money or out-of-the-money, have their entire premium as the time value. Accordingly,

Time value of a call = C – [max (0, S - E)]Time value of a put = C – [max (0, E - S)]

Example:Consider the following data calls on a hypothetical stock.

Option

Exercise Price (Rs)

Stocks Price (Rs)

Call Option Price (Rs) Classification

1. 80 83.50 6.75 In-the-money2. 85 83.50 2.50 Out-the-money

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We may show how the market price of the two calls can be divided between intrinsic and time values.

Option S E C Intrinsic Value Max (0,S-E)

Time Value C-max (0,S-E)

1. 83.50 80 6.75 3.50 6.75-3.50=3.252. 83.50 85 2.50 0 2.50-0=2.50

COVERED AND UNCOVERED OPTIONSAn option contract is considered covered if the writer owns the underlying asset or has another

offsetting option position. In the absence of one of these conditions, the writer is exposed to the risk of having to fulfill the contractual obligations by buying the asset at the time of delivery at an unfavorable price.

The call writer may have to purchase the underlying asset at a price that is higher than he strike price. The put writer may have to buy the asset from the holder at a price that creates a loss. When they face such a risk writers are said to be uncovered (or naked).

Covered Call Options / Covered CallsCall writers are consider to be covered if they have any of the following positions:

Along position in the underlying asset. An escrow-receipt from a bank. A security that is convertible into requisite number of shares of the underlying security. A warrant exercisable for requisite number of shares of the underlying security. A long position in a call on the same security that has the same or the lower strike price and

that expires at the same time or later than the option being written.Covered Put

There is only one way for put writer to be covered. They must own a put on the same underlying asset with the same or later expiration month and the higher strike price than the option being written.

MARGIN REQUIREMENTSAs in the case of futures contracts, the performance of contracts is also assured by the options

exchanges (the OCC) the buyer of an option enjoys the right of its performance exchange, the exchange has, in turn, to make sure that the contract will be honoured. Thus, for example, if I write a naked call, my broker would need a guarantee in some form that I would have the necessary funds to be able to deliver the asset, should the buyer of the option choose to exercise the call, and in turn assure the exchange of the performance of the contract. For this, margin requirements exist as a form of collateral to ensure that the writer of a naked call can fulfill the terms of the contract.

Accordingly, the writers of options are required to meet the margin requirements. The requirements vary depending upon the brokerage firm, the price of the underlying asset, the price of the option, and whether the option is a call or a put. As a general rule, initial margins are at least 30% of the stock price when the option is written, plus the intrinsic value of the option. The amount of margin has an influence on the degree of financial leverage that the investor has and, consequently, on the returns and risk on the position.

13


risk and return equity stock options

We will now see the risk and return associated with equity stock options.

CALL OPTIONSConsider a call option on a certain share; say ABC Suppose the contract is made between two

investors X and Y, who take, respectively, the short and long positions. The other details are given below:Exercise price = Rs 120Expiration month = March, 2001Size of contract = 100 sharesDate of entering into contract =January 5, 2001Price of share on the date of contract = Rs 124.50Price of option on the date of contract = Rs 10

At the time of entering in to the contract, Investor X writes a contract and receives Rs. 1000 (= 10 x 100) Investor Y takes a long position and pays Rs 1000 for it.

On the date of maturity, the profit or loss to each investor would depend upon the price of the share ABC prevailing on that day. The buyer would obviously not call upon the call writer to sell shares if the price happens to be lower than Rs 120 per share. Only when the price exceeds Rs 120 per share will a call be made. Having paid Rs 10 per share for buying an option, the buyer can make a profit only in case the share price would be at a point higher than Rs 120 + Rs 10 = Rs 130. At a price equal to Rs 130 a break-even point is reached. The profit/loss made by each of the investors for some selected values of the share price of ABC is indicated below.

Profit / Loss Profile for the Investors - Call Option Possible Price of ABC at

Call Maturity (Rs.) Investor X Investor Y

90 1000 -1000100 1000 -1000110 1000 -1000120 1000 -1000130 0 0140 -1000 1000150 -2000 2000160 -3000 3000

The profit profile for this contract is indicated below. Figure (a) shows the profit/loss function for the investor X, the writer of the call, while Figure (b) gives the same for the other investor Y, the buyer of the option.

(a) For Investor X

14

Profit

1500 –

1000 –

500 –

0

500 –

1000 –

1500 –

2000 –

2500 –

Loss

90 100 110 120 130 140 150 160

Stock Price


(b) For Investor Y

It is evident that the call writer's profit is limited to the amount of call premium but, theoretically, there is no limit to the losses if the stock price continues to increase and the writer does not make a closing transaction by purchasing an identical call. The situation is exactly opposite for the call buyer for whom the loss is limited to the amount of premium paid. However, depending on the stock price, there is no limit on the amount of profit which can result for the buyer. Being a 'zero-sum' game, a loss (gain) to one party implies an equal amount of gain (loss) to the other party.

PUT OPTIONSIn a put option, since the investor with a long position has a right to sell the stock and the writer

is obliged to buy it at the will of the buyer, the profit profile is different from the one in a call option where the rights and obligations are different.Consider a put option contract on a certain share, PQP, Suppose, two investors X and Y enter into a contract and take short and long positions respectively. The other details are given below: Exercise price = Rs I 10 Expiration month = March, 2001 Size of contract= I 00 shares Date of entering into contract =January 6, 2001 Share price on the date of contract = Rs 1 12

15

Profit

3000 –

2500 –

2000 –

1500 – 1000 –

500 –

0 –

500 –

1000 –

1500 –

Loss

90 100 110 120 130 140 150 160

Stock Price

Make Your Future With Options Price of put option on the date of contract = Rs 7.50

Now, as the contract is entered into, the writer of the option, X will receive Rs 750 (=7.50 x 100) from the buyer, Y At the time of maturity, the gain/loss to each party depends on the ruling price of the share. If the price of the share is Rs 110 or greater than that, the option will not be exercised, so that the writer pockets the amount of put premium-the maximum profit which can accrue to a seller. At the same time, it represents the maximum loss that the buyer is exposed to. If the price of the share falls below the exercise price, a loss would result to the writer and a gain to the buyer. The maximum loss that the writer may theoretically be exposed to is limited by the amount of the exercise price. Thus, if the value of the underlying share falls to

16


zero, the loss to the writer is equal to Rs. 110 – Rs. 7.50 = Rs. 102.50 per share. The profit/loss for some selected values share are given below.

Possible Price of PQR at Investor X Investor Y Put Maturity (Rs) Investor X Investor Y

80 -2250 225090 -1250 1250

100 -250 250110 750 -750120 750 -750130 750 -750140 750 -750150 750 -750

The break-even share price would be Rs 102.50 (= Rs 110 Rs 7.50). If the price of the share happens to be lower than this, the writer would make a loss-and the buyer makes a gain. For instance, when the price of the share is Rs 100, the gain/loss for each of the investors may be calculated as shown below.

Investor XOption premium received = 7.5 x 100 = Rs. 750

Amount to be paid for shares = 110 x 100 = Rs. 11000Market value of the shares = 100 x 100 = Rs. 10000Net Profit(Loss) = 750 - 11000 + 10000 = (Rs. 250)

Investor YOption premium paid = 7.5 x 100 = Rs. 750Amount to be received for shares = 110 x 100 = Rs. 11000Market value of the shares = 100 x 100 = Rs. 10000 Net profit(loss) = -750 + 11000 - 10000 = Rs. 250

The profile of profit/loss for each of the investors is given in Figures below. Fig. (a) shows the profit/loss function for the investor X the writer of the put, while the Fig. (b) gives the same for the other investor Y, the buyer of the option. As indicated earlier, the profiles of the two investors replicate each other.

(a) For investor X

17

Profit

1500 –

1000 –

500 –

0

500 –

1000 –

1500 –

2000 –

2500 –

3000 –

Loss

90 100 110 120 130 140 150 160

Stock Price


(b) For Investor Y

18

Profit

2500 –

2000 –

1500 – 1000 –

500 –

0 –

500 –

1000 –

Loss

90 100 110 120 130 140 150

Stock Price


OPTIONS TRADING STARTEGIES

We have considered above the profit/loss resulting to the investors with long and short positions in the call and put options. It is important to note that an investor need not take positions in naked options only or in a single option alone. In fact, a number of trading strategies involving options may be employed by the investors. Options may be used on their own, in conjunction with the futures contracts, or in a strategy using the underlying instrument (equity stock, for example). One of the attractions of options is that they could be used for creating a very wide range of payoff functions. We now discuss some of the commonly used strategies.

To begin with, we may consider investment in a single stock option. The payoffs associated with a long or short call, and a long or short put option has already been discussed. A long call is used when one expects that the market would rise. The more bullish market sentiment or perception, the more out-of-the money option should one buy. For the option buyer in this strategy, the loss is limited to the premium payable while the profit is potentially unlimited. On the other hand, the writer of a call has a mirror image position along the break-even line. The writer writes a call with the belief or expectation that the market would not show an upward trend.

In case of the put option, a long put would gain value as the underlying asset, the equity share price or the market index, declines. Accordingly, a put is bought when a decline is expected in the market. The loss for a put buyer is limited to the amount paid for the option if the market ends above the option exercise price. The writer of a put option would get the maximum profit equal to the premium amount but would be exposed to loss should the market collapse. The maximum loss to the writer of a put option on an equity hare could be equal to the exercise price (since the stock price cannot be negative).

Thus, while selling of options may be used as a legitimate means of generating premium income and bought in the expectation of making profit from the likely bullish / bearish market sentiments, they may or may not be used alone. They may, however, be combined in several Ways without taking positions in the underlying assets or they might be used in conjunction with the underlying assets for purposes of hedging, which we describe in the next section.

HEDGING USING CALL AND PUT OPTIONSHedging represents a strategy by which an attempt is made to limit the losses in one position by

simultaneously taking a second offsetting position. The offsetting position may be in the same or a different security. In most cases, the hedges are not perfect because they cannot eliminate all losses. Typically, a hedge strategy strives to prevent large losses without significantly reducing the gains.

Very often, options in equities are employed to hedge a long o short position in the underlying common stock. Such options are called covered options in contrast to the uncovered or naked options, discussed earlier.

Hedging a Long Position in Stock An investor buying a common stock expects that its price would increase. However, there is a

risk that the price may in fact fall. In such a case, a hedge could be formed by buying a put i.e., buying the right to sell. Consider an investor who buys a share for Rs. 100. To guard against the risk of loss from a fall in its price, he buys a put for Rs. 16 for an exercise price of, say, Rs. 110. He would, obviously, exercise the option only if the price of the share were to be less than Rs. 110. Table below gives the profit/loss for some selected values of the share price on maturity of the option. For instance, at a share price of Rs. 70, the put will be exercised and the resulting profit would be Rs. 24, equal to Rs. 110 – Rs. 70, or Rs 40 minus the put premium of Rs. 16. With a loss of Rs. 30 incurred for the reason of holding the share, the net loss equals to Rs. 6.

19


Profit / Loss for Selected Share Values: Long Stock Long PutSharePrice

ExercisePrice

Profit onExercise (i)

Profit / Loss onShare Held (ii)

Net Profit(i) + (ii)

70 110 24 -30 -6

80 110 14 -20 -6

90 110 4 -10 -6100 110 -6 0 -6110 110 -16 10 -6120 110 -16 20 4130 110 -16 30 14140 110 -16 40 24

The profits resulting from the strategy of holding a long position in stock and long put are shown in the figure below.

Hedging: Long Stock Long Put

Hedging a Short Position in Stock Unlike an investor with a long position in stock, a short seller of stock anticipates a decline in

stock price. By shorting the stock now and buying it at a lower price in the future, the investor intends to make a profit. Any price increase can bring losses because of an obligation to purchase at a later date. To minimize the risk involved, the investor can buy a call option with an exercise price equal to or close to the selling price of the stock.

Let us suppose, an investor shorts a share at Rs. 100 and buys a call option for Rs. 4 with a strike price of Rs. 105. The conditional payoffs resulting from some selected prices of the share are shown in a table below.

Profit / Loss for Selected Share Values: Short Stock Long CallSharePrice

ExercisePrice




90 105 -4 15 11

20

Profit on Exercise of Put Profit

50 - 40 -

30 -20 - 10 -

0 10 -20 -30 -

40 - Loss

Stock Price

Profit / Loss on Hedging

Profit / Loss on Long Stock

E


95 105 -4 10 6100 105 -4 5 1105 105 -4 0 -4110 105 1 -5 -4115 105 6 -10 -4120 105 11 -15 -4

The payoff function associated with this policy is shown below.

Hedging : Short Stock Long Call

HEDGING WITH WRITING CALL AND PUT OPTIONSBoth the strategies discussed above aim at limiting the risk of an underlying position in an

equity stock. Options may also be used for enhancing returns from the positions in stock. If the common stock is not expected to experience significant price variations in the short run, then the strategies of writing calls and puts may be usefully employed for the purpose. As an example, suppose that you hold shares of a stock which you expect will experience small changes in the short term, then you may write a call on these. This is known as writing covered calls. By writing covered call options, you tend to raise the short-term returns. Of course, you will not derive any benefit if large price changes occur because then the option will be exercised or, else, you would have to make a reversing transaction. The writing of covered calls, i.e., agreeing to sell the stock you have, is a very conservative strategy.

To illustrate the strategy of writing a covered call, consider an investor who has bought a share for Rs 100, and who writes a call with an exercise price of Rs. 105, and receives a premium of Rs. 3. The profit/loss occurring at some prices of the underlying share is indicated in table below.

Profit / Loss for Selected Share Values: Long Stock Short CallSharePrice

ExercisePrice




90 105 3 -10 -795 105 3 -5 -2

21

Profit 50 -

40 -

30 -20 - 10 -

0 10 -20 -30 -

40 - Loss

Stock Price


Profit / Loss on Short Stock Profit / Loss on Call Option

E


100 105 3 0 3105 105 3 5 8110 105 -2 10 8115 105 -7 15 8120 105 -12 20 8

Figure depicts the payoff function for the strategy of writing covered calls.

Hedging : Long Stock Short Call

In a similar way, an investor who shorts stock can hedge by writing a put option. By undertaking to ‘be the buyer’, the investor hopes to reduce the magnitude of loss that would be occurring from an increase in the stock price, by limiting the profit that could be made when the stock price declines. As an example, suppose that you short a share at Rs. 100 and write a put option for Rs. 3, having an exercise price of Rs. 100. Clearly, the buyer of the put will exercise the option only if the share price does not exceed the exercise price. The conditional payoffs resulting from some selected values of the share price are contained in table below.

Profit / Loss for Selected Share Values: Short Stock Short PutSharePrice

ExercisePrice




90 100 -7 10 395 100 -2 5 3

100 100 3 0 3105 100 3 -5 -2110 100 3 -10 -7115 100 3 -15 -12120 100 3 -20 -17

22

Profit 50 -

40 -

30 -20 - 10 -

0 10 -20 -30 -

40 - Loss

Stock Price


Profit / Loss on Long Stock

Profit / Loss on Call Option

E


The figure below gives a general view of the profit function associated with the policy of writing a protected put.

Hedging : Short Stock Short Put

23

Profit / Loss on Short Stock Profit 50 -

40 -

30 -20 - 10 -

0 10 -20 -30 -

40 - Loss

Stock Price


Profit / Loss on Put Option

E

Make Your Future With OptionsSPREADS

A spread trading strategy involves taking a position in two or more options of the same type.

Bull SpreadsOne of the most popular spread strategies is a bull spread. A bull spread reflects the bullish

sentiment of a trader and can be created by purchasing a call option on a stock and selling another call on the stock and with the same expiry but a higher exercise price. At expiry, if the stock remains below the lower strike price, both calls would expire unexercised and the loss will be limited to the initial cost of the spread. It may be recalled that other things remaining the same, a call with a lower exercise price has a greater premium. Accordingly, the price payable for buying a lower exercise price option is more than the premium receivable from writing an option with a greater exercise price and, hence, a cost is involved in buying the spread.

Further, if the stock price rules between the strike prices of the two calls, the purchased call is in-the-money while the call sold expires unexercised. Thus, the payoff equals the difference between the stock price and the (lower) exercise price. If the stock price is greater than higher exercise price, both options are in-the-money and the payoff equals the difference between the exercise prices of the two options.

To illustrate this suppose that you buy a call option with an exercise price of Rs. 50 for Rs. 8 and sell one with an exercise price of Rs. 60 for a premium of Rs. 2, both being on the same stock and with same expiration date. Now if the price rules at Rs. 50 or less, none of them would be exercised, with the result that the payoff will be nil and net loss would be Rs. 6 (Rs. 8 – Rs. 2).

If the price of stock at the time of exercise is, say, Rs. 58, then the call with an exercise price of shall be exercised for a payoff of Rs. 58 – Rs. 50 =Rs. 8, the net being Rs. 8 – Rs. 8 + Rs. 2 = Rs. 2.

Finally, if the price of the stock is higher than Rs. 60, both of these will be exercised and the payoff be Rs. 60 – Rs. 50 = Rs. 10 with the net profit equal to Rs. 10 - Rs 6 = Rs. 4.

The payoffs resulting from a bull spread strategy are given below. While E l and E2 are the respective strike prices of the calls that are long and short, S1 represents the stock price at the time of exercising the calls.

Payoffs from a Bull Spread (Using Calls)Price of Stock Payoff from

Long CallPayoff fromShort Call Total Payoff

S1 > E2 S1 – E1 E2 – S1 E2 – E1

E1 < S1 < E2 S1 – E1 0 (NE)* S1 – E1

S1 <= E1 0 (NE) 0 (NE) 0*NE = Not Exercised

Bull Spread (Using Calls)

Thus, by selling a call against an otherwise naked call, the investor in a bull spread sacrifices an unlimited profit potential in return for the initial cost. If both the calls are initially out-of-the-money,

24

Profit

Loss

Profit / Loss on Long Call

E1 E2

Stock Price

Profit / Loss on Short Call

Make Your Future With Optionsthen a small cost would be involved in creating the spread which would be aggressive in nature. A less bullish investor would buy an in-the-money spread for lower gearing. A spread with one call initially in-then-money and the other one initially out-of-the-money would be relatively less aggressive than a spread with both calls being out-of-the-money, while a spread created with both calls being in-the-money initially would be the most conservative.

A bull spread can also be created using puts. One put is purchased and another one is sold which is on the same stock, with the same expiry date but with a higher exercise price. On expiry, if the stock remains below the lower exercise price, both options are exercised and the position is closed for the difference between the two exercise prices. This results in an overall loss of the initial credit (higher premium received on short put minus lower premium paid on long put) minus the difference. If the stock price is between the two exercise prices, the put with the lower exercise price would expire unexercised resulting in a net profit equal to the initial credit minus the difference between the exercise price and the stock price. For the stock prices exceeding the higher exercise price, both puts expire unexercised leading to no payoffs and a net profit equal to the initial credit.

Suppose an investor buys a put option with an exercise price equal to Rs. 40 for Rs. 6 and writes an option identical in all respects except the exercise price that is equal to Rs. 50, for a price of Rs. 9. This spread gives an initial credit of Rs. 3. Now, if the stock price is less than Rs. 40, then both options are in-the-money and can be exercised. A commitment to buy at Rs. 50 and to sell at Rs. 40 implies an outward payoff of Rs. 10 and a net loss equal to Rs. 10 – Rs. 3 = Rs. 7. For a stock price in between the two exercise prices, say Rs. 44, the investor has to buy the stock at Rs. 50 and thus lose Rs. 6 on the option. In this case, the net loss would equal Rs. 6 – Rs. 3 = Rs. 3. Similarly, when the stock price would be more than Rs. 50, none of the options will be exercised and a net profit of Rs. 3 will be made.

In general, the profit function is as shown in the figure. The payoffs associated with a bull spread created using put options are given in the table. The stock price at the time of exercise is given by S1 and the two options have exercise prices of El and E2 (E2 > El).

Payoffs from a Bull Spread (Using Puts)Price of Stock Payoff from

Long PutPayoff fromShort Put Total Payoff

S1 <= E2 E1 – S1 S1 – E2 E1 – E2

E1 < S1 < E2 0 S1 – E2 S1 – E2

S1 >= E2 0 0 0

Bull Spread (Using Puts)

Example:

Type of OptionExercise Price of option Premium on Option

Purchased Sold Purchased Sold(a) Call 60 75 10 4

25

Stock Price

E1

Profit

Loss

Profit / Loss from Long Put

Profit / Loss from Short Put

E2


(b) Put 50 65 4 11

(a) CallWith price of long call, E1 = 60 and price of a short call, E2 = 75, the profit/loss would be as follows:

Stock Price Payoff from Long Call

Payoff fromShort Call Total Payoff Net Profit / Loss

= Payoff – CostS1 > = E2 S1 – 60 75 – S1 15 15 – 6 = 9

E1 < S1 < E2 S1 – 60 0 S1 – 60 S1 – 60 – 6 = S1 - 54S1 < = E1 0 0 0 0 – 6 = -6

The break-even stock price would be one where net profit is equal to zero. Accordingly, S1 - 54 = 0 or S1= 54. Thus, a stock price greater than Rs. 54 would yield profit.

(b) PutBuying a put option with exercise price equal to Rs. 50 and selling a put option with a greater exercise price of Rs. 65 represents a bull spread. This would result in a positive cash flow of Rs. 11 – Rs. 4 = Rs. 7 to the investor up front.

The profit/loss position is as given below.


Payoff fromShort Call

Total Payoff

Net Profit / Loss= Payoff – Cost

S1 > = E2 0 0 0 0 + 7 = 7E1 < S1 < E2 0 S1 – 65 S1 – 65 S1 – 65 + 7 = S1 – 58

S1 < = E1 50 – S1 S1 – 65 - 15 - 15 + 7 = - 8To obtain the break-even price, we set S1 - 58 = 0, so that, S1 = 58, implying that a profit would

result when the stock price exceeded Rs. 58 and a loss would be incurred when it fell short of Rs 58.

Bear Spreads In contrast to the bull spreads, bear spreads are used as a strategy when one is bearish of the

market, believing that it is more likely to go down than up. Like a bull spread, a bear spread may be created by buying a call with one exercise price and selling another one with a different exercise price. Unlike in a bull spread, however, the exercise price of the call option purchased is higher than that of the call option sold. A bear spread would involve an initial cash inflow since the premium for the call sold would be greater than for the call bought. Assuming that the exercise prices are E1 and E2 with E1 < E2, the payoffs realizable from a bear spread in different circumstances are given in the table below. The profit profile is shown in figure.

Payoffs from a Bear Spread (Using Calls)Price of Stock Payoff from

Long CallPayoff fromShort Call Total Payoff

S1 >= E2 S1 - E2 E1 - S1 E1 – E2

E1 < S1 < E2 0 E1 – S1 E1 – S1

26


S1 >= E2 0 0 0

Bear Spread (Using Calls)

Suppose that the exercise prices of two call options are Rs. 50 and Rs. 60. If the stock price, S 1, were lower than Rs. 50, then none of the calls will be exercised and, therefore, no payoffs are involved. If the price were between the two exercise prices, say Rs. 57, then the call written for Rs. 50 would be exercised and the investor loses Rs. 7, and if the price of the stock exceeded Rs. 60, both the calls would be exercised and an outward payoff of Rs. 10 would result. In each of the cases, the net profit would be obtained by adjusting for the initial cash inflow.

Bear spreads can also be created by using put options instead of call options. In such a case, the investor buys a put with a high exercise price and sells one with a low exercise price. This would require an initial investment because the premium for the put with a higher exercise price would be greater than the premium receivable for the put with the lower exercise price, written by the investor. In this spread, the investor buys a put with a certain exercise price and chooses to give up some of the profit potential by selling a put with a lower exercise price. In return for the profit given up, the investor gets the price of the option sold.

The payoffs from a bear spread created with put options are given in the table below, wherein E1 and E2 are the exercise prices of the option sold and purchased respectively. The profit function is given in figure below. It may be observed that, like bull spreads, bear spread limit both the upside profit potential and the downside risk.

Payoffs from a Bear Spread (Using Puts)Price of Stock Payoff from

Long PutPayoff fromShort Put Total Payoff

S1 >= E2 0 0 0E1 < S1 < E2 E2 - S1 0 E2 – S1

S1 >= E2 E2 - S1 S1 – E1 E2 – E1

Bear Spread (Using Puts)

27

Stock Price E1

Profit

Loss

Profit/Loss from Long Call

Profit/Loss from Short Call

E2

Stock Price

E1

Profit

Loss

Profit/Loss from Long Put

Profit/Loss from Short Put

E2


Example:

Type of OptionExercise Price of option Premium on Option

Purchased Sold Purchased Sold

(a) Call 80 70 5 11(b) Put 70 60 9 5

(a) CallHere El is the price of call sold and E2 is the price of the call purchased. Thus, E l = 70 and E2 = 80. Net premium obtained = 11 - 5 = Rs. 6. The profit/loss would be as shown below:



Total Payoff


S1 > = E2 S1 – 80 60 – S1 - 20 - 20 + 6 = - 14E1 < S1 < E2 70 – S1 0 70 – S1 70 – S1 + 6 = 76 – S1

S1 < = E1 0 0 0 0 + 6 = 6

To determine break-even stock price, we set 76 – S1 = 0. Thus, S1 = 76. Therefore, a stock price below Rs. 76 would yield profit, while for stock prices above this level losses would result.

(b) PutWith El = 60 and E2 = 70, and a net cost of Rs. 4 (= Rs. 9 – Rs. 5), the profit/loss profile is as given below.



Total Payoff


S1 > = E2 0 0 0 f0 - 4 = - 4E1 < S1 < E2 0 60 – S1 60 – S1 60 – S1 - 4 = 56 – S1

S1 < = E1 70 – S1 S1 - 60 10 10 - 4 = 6

For the break-even price, 56 – S1 = 0. Thus, S1 = 56. With stock prices below Rs. 56, profit will result, while loss will result with prices greater than this.

Butterfly Spreads While bull and bear spreads involve taking positions in two options, a butterfly spread results

from positions in options with three different strike prices. This involves buying a call option with a relatively low exercise price, El, buying another call option with a relatively large exercise price, E3, and selling two call options with a strike price, E2 which is halfway between El and E3. The price E2 is usually close to the current stock price, with the result that a profit results if the stock price stays

28

Make Your Future With Optionsclose to E2 and a small loss would be incurred if there is a significant price movement either way from it. The strategy is obviously meant for an investor who feels that large price changes are unlikely. The positions taken in the strategy involve some cost.

If El, E2 and E3 be Rs. 50, Rs. 60 and Rs. 70 respectively, and the stock price be less than Rs. 50, then, clearly, no call will be exercised. Accordingly, the total loss equals the initial cost involved. Similarly, beyond Rs. 70, when all calls will be exercised, the total loss equals the initial cost, because the gain on the options with long position will be exactly offset by a corresponding loss on the twin options written. Gain would result when the stock price is between Rs. 50 and Rs. 60, and shall be higher as the price moves towards Rs. 60. Beyond this price, the amount of gain would decline with an increase in the stock price up to the level of Rs. 70. The payoffs for a butterfly spread are given in the table below. The profit/loss profile for a butterfly spread is given in the figure.

Payoffs from a Butterfly Spread Price of Stock

Payoff fromFirst Long Call

(E1)

Payoff from Second Long Call

(E3)

Payoff fromShort Calls

(E2)TotalPayoff

S1 < E1 0 0 0 0E1 <= S1 < E2 S1 – E1 0 0 S1 – E1

E2 <= S1 < E3 S1 – E1 0 2(E2 - S1) E3 – S1*S1 >= E2 S1 – E1 S1 – E3 2(E2 - S1) 0

S1 - E1 + 2E2 - 2S1 = 2E2 – E1 – S1, or E3 – S1 Since 2E2 = E3 + E1Butterfly Spread

Example:

A certain stock is selling currently at Rs. 72. An investor, who feels that a significant change in this price is unlikely, in the next three months, observes the

29

Stock Price

E1

Profit

Loss

Profit / Loss from Long CallProfit / Loss from

Short Calls

E 2

Profit / Loss from Long Call

E3 33


market prices of 3-month calls as tabulated below:

Exercise Price Call Price (Rs.)65 1170 875 6

The investor decides to go long in two calls—one each with exercise price Rs. 65 and Rs. 75—and writes two calls with an exercise price of Rs. 70. Lets see the payoff function for different levels of stock prices. (i) Rs. 63 (ii) Rs. 68 (iii) Rs. 73 (iv) Rs. 80

The decision of the investor leads to a butterfly spread. Buying two calls involves a payment of Rs. 11+ Rs. 6 = Rs. 17, and writing two calls yields Rs. 8 x 2 = Rs.16. Thus, cost involved with the package of options = Rs. 17 – Rs. 16 Re. 1. The payoffs associated with this plan are given below.

Payoffs from a Butterfly Spread

Price of StockPayoff from

First Long Call (E1 = 65)

Payoff from Second Long Call (E3 = 75)

Payoff fromTwo Short Calls

(E2 = 70)TotalPayoff

S1 < 65 0 0 0 065 <= S1 < 70 S1 – 65 0 0 S1 – 6570 <= S1 < 75 S1 – 65 0 2(70 - S1) 75 – S1

S1 >= 75 S1 – 65 S1 – 75 2(70 - S1) 0From the table, it is clear that when the stock price is less than Rs. 65 or Rs. 75 and above, the

payoff will be nil, while if the price varied between Rs. 65 and Rs. 70, the payoff equal to the price in excess of Rs. 65 and if it is in the range of Rs. 70 to Rs. 75, then the payoff is Rs. 75 minus the stock price. Accordingly, profit/loss can be calculated for various given prices as follows.

Price Total payoff from Calls Cost of Strategy Net Profit / Loss

63 0 (1) (1)68 3 (1) 273 2 (1) 180 0 (1) (1)

COMBINATIONSWhile spreads involve taking positions in call or put options only, combinations represent option

trading strategies which involve taking positions in both calls and puts on the same stock. Important combination strategies include straddles, strips, straps and strangles.

Straddle A straddle involves buying a call and a put option with the same exercise price and date of

expiration. Since a call and a put are both purchased, it costs to buy a straddle and, to that extent, a loss is incurred if the price does not move away from the exercise price since none of them will be exercised. The payoff and profit function is respect of a straddle are shown below.

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Make Your Future With OptionsPayoffs from a Straddle

Exercise Price Range

Payoff fromLong Call

Payoff fromShort Call Total Payoff

S1 <= E 0 E - S1 E – S1

S1 > E S1 - E 0 S1 - EStraddle

From the profit function depicted in the figure, it is evident that buying a straddle is an appropriate strategy to adopt when large price changes are expected in the stock - for lower prices of the stock, the put option will be exercised and for higher prices, the call option will be exercised.

Suppose an investor feels that the price of a certain stock, currently valued at Rs. 85 in the market, is likely to move significantly, upward or downward, in the next three months. The investor can create a straddle by buying a call and a put option both with an exercise price of Rs. 85 and an expiration date in three months. Suppose that the call costs Rs. 4 and the put Rs. 2. Now, if the stock price at expiration is Rs. 85, then none of the options will be exercised and a loss of Rs. 6 would occur. If the stock price jumps to Rs 100, then the call will be exercised resulting in a net profit of (Rs. 100 – Rs. 85) – Rs 6 = Rs. 9 while if the price falls to, say, Rs. 57 then the put option will be exercised and a net profit of Rs. 85 – Rs. 57 – Rs. 6 = Rs. 22 will result.

This kind of strategy is an obvious one to employ in respect of the stock of a company, which is subjected to a takeover bid. The straddle shown above is an example of a straddle purchase. This is also referred as a bottom straddle. A straddle write, or a top straddle represents the reverse position so that it may be created by selling a call and a put with the same expiration date and exercise price. In a straddle write, a significant profit is made if stock price is equal to, or close to exercise price, but large deviations of stock price from this on either side would cause large losses, which are potentially unlimited. Hence, a straddle write is a very risky strategy to adopt.Strips

A strip results when a long position in one call is coupled with a long position in two puts, all with the same exercise price and expiration date. Here the investor is expecting that a big price movement in the stock price will take place but a decrease in the stock price is more likely than an increase. Since a put option is profitable when the price decreases, two puts are bought in this strategy. Accordingly, the profit function for the strategy, shown in the figure below is steeper in the lower than exercise price range and less steep in region of higher prices.

Strip

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Profit

Loss

E Stock Price


StrapsOn the other hand, if the investor is expecting that a big price change would occur in the stock

price, but feels that there is a greater likelihood of the price increasing rather than decreasing, the investor will consider the strategy of a strap. A strap consists of a long position in two calls and one put with same exercise price and expiry date. The profit function of a strap are shown below.

Strap

StranglesIn a strangle, an investor buys a put and a call option with the same expiration date but with

different exercise prices. The exercise price of the put is lower than the exercise price of the call, so that a profit would result if the stock price is lower than the exercise price of the put or if the stock price exceeds the call exercise price. Between the two exercise prices, none of the options is exercised and hence, a net loss, equal to the sum of the premia paid for buying the two options, results. It follows, then, that a strangle is an appropriate strategy for adoption when the price is expected to move sharply. The profit function, for exercise prices E l and E2of put and call respectively, is shown below and payoffs for different ranges of the stock price are given in the table.

Payoffs from a StranglePrice of Stock Payoff from Put Payoff from Call Total Payoff

S1 <= E1 E1 – S1 0 E1 – S1

E1 < S1 < E2 0 0 0S1 >= E2 0 S1 – E2 S1 – E2

Strangle

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Profit

Loss

E

Stock Price

Profit

Loss

E

Stock Price

Profit

Loss

E1 E2 Stock Price

Profit / Loss from Call Option

Profit / Loss from Put Option


Evidently, a strangle is a similar strategy to a straddle, because here as well the investor is betting that a large price change would take place but is not sure as to the direction in which the change would occur. However, in a strangle, the stock price has to move farther, than in a straddle, in order that the investor makes a profit. Also, if the stock price happens to be between the two exercise prices, the downside risk is smaller with a strangle than it is with a straddle if the price is close to the exercise price.

The strangle described above is also called the bottom vertical combination or strangle bought or long strangle. Similarly, a strangle may be sold. A short strangle is the choice of an investor who believes that large variations in stock price are unlikely. However, if they do occur, then larger amounts of losses are imminent.CONDORS

A condor is an investment strategy which involves four call options or four put options. It may be long condor or a short condor.

Long CondorA long condor involving call options is created by buying calls—one with a very low exercise

price E1, and another with a comparatively high exercise price E4, - and selling two call options—one with a price E2 higher than, and closer to, E1, and the other with a price E3 which is lower than and closer to E4, E1, E2, E3 and E4 are chosen in such a way that E2 – E1 = E4 – E3 and E3 – E1 = 2(E2 – E1).The profit function of a long condor is shown below:

Long Condor

A long condor using put options can be created similarly, by buying one put with exercise price E1 and another one with an exercise price of E4, and selling two puts—with exercise prices of E2 and E3. The prices E1, E2, E3 and E4 are related to each other as in the case of a long condor with call options.Short Condor

A short condor results by reversing the above strategy, and involving selling two calls having exercise prices of E1 and E4, and buying two calls with exercise prices of E2 and E3. Figure depicts the profit / loss associated with this policy.

Short Condor

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Stock Price E1

Profit

Loss


E 2


E 4

E 3

Profit / Loss from Short CallProfit / Loss from

Short Call

Stock Price

E1

Profit

Loss


E 2


E 4

E 3

Profit / Loss from Short CallProfit / Loss from

Short Call


An examination of the profit functions for condors and strangles reveals that while profit/loss potential resulting from large deviations in stock price is very high for a strangle, it is not so in the case of a condor. In the latter case, profit/loss is limited.

BOX SPREADS In a box spread strategy, the profit or loss made is independent of the stock price. With the

objective of making a profit regardless of the stock price, a box spread may be created in many ways. For instance, it may be decided to buy one call and write one put, with an exercise price equal to E1, and write one call and buy one put, with an exercise price of E2 (E2 > El). The table shows that the payoff in respect of this strategy will be the same irrespective of the price of the stock.

Payoffs from Box Spreads

Stock Price Range

Exercise Price = E1 Exercise Price = E2TotalCall

Bought Put Sold Call Sold Put Bought

S1 < =E1 0 S1-E1 E2-S1 0 E2-E1E1 < S1 < E2 S1-E1 0 0 E2-S1 E2-E1

S1 > = E2 S1-E1 0 E2-S1 0 E2-E1When the stock price does not exceed the lower exercise price of E1, none of the call options is

exercised and both the puts are exercised. This results in a total payoff of E2 - El because the stock bought for E1 is sold for E2. Similarly, when the stock price is E2 or more, none of the puts is exercised. With a right to buy the stock at El and the obligation to sell at E2, the two call options result in a payoff of E2 – E1. For the price range between E1 and E2, stock will be bought at El, using the right under long call to buy at this price, and sold for E2, by exercising the right to sell the stock by virtue of the put option.

A box spread can also be constructed by buying a put and writing a call, with an exercise price El, and buying a call and writing a put with an exercise price of E2 (E2 being greater than El).

There are certain fundamental differences between a futures and an option contract.

OPTIONS FUTURES

Only the seller is obligated to perform

Both the parties are obligated to perform

Premium is paid by the buyer to No premium is paid by any party34

Make Your Future With Optionsthe seller

Loss is restricted while there is unlimited gain potential for the option buyer

There is potential / risk for unlimited gain / loss for the futures buyer

Options prices are affected not only by prices of the underlying asset but also the time remaining for expiry of the contract and volatility of the underlying asset

Future prices affected mainly by the underlying asset

Option contract can be exercised any time till the maturity by the buyer

Future contract can be honoured by both the parties only on the date specified

The Indian Capital Market has witnessed impressive growth and qualitative changes, especially over the last two decades. Derivatives are playing a crucial role in the Capital Markets world-wide. Their introduction in the Indian Capital Market is, the beginning of a new era….. Derivatives are for emerging markets like India. They work as instruments for risk management and tools for market development and serve to enhance market efficiency in areas of risk transfer.

Securities and Exchange Board of India (SEBI) after considering the suggestions of the Committee on Derivatives, chaired by Mr. L. C. Gupta & of Mr. J. R. Varma in their reports stipulated the regulatory framework and risk containment measures for derivatives trading in India. In line with SEBI directives, the National Stock Exchange of India Limited (NSE) commenced trading in index futures on June 12, 2000. Trading in Index Options commenced on June 4, 2001. Futures & Options contracts on Index are based on the popular benchmark S&P CNX Nifty. NSE also became the first Exchange to launch trading in options on individual securities from July 2, 2001. Bombay Stock Exchange (BSE) too began trading in index futures in June last year and soon after NSE started its trading in stock options BSE also began its option trading. Options on individual securities are available on 53 securities stipulated by SEBI. As the derivatives market is in its nascent stage in India as compared to other countries. The volume being traded in futures and options used to be very low, however it has picked up significantly in last one year since the bull run began and now daily derivatives volumes is more then 2 times the daily cash volume.

Both BSE and NSE have been taking measures to spread awareness through investor education programs. They have seminars and workshops on a regular basis where they teach people about futures and options, how to deal in them and try and clear their myths regarding them. And finally these results are being reflected in the market.

The National Stock Exchange is emerging the most-preferred exchange for investors in the newly-launched derivatives products - futures and options trading. Volumes in futures and options trading on NSE have been 30-35 times higher than that on its arch-rival, the Bombay Stock Exchange.

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