option and greeks (derivatives)

8/8/2019 option and greeks (derivatives)

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Options & Greeks

Project submitted by:

Judevino 07

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INDEX

Sr. no. TOPIC Page no.

1. What is an option? 32. What are call options? 3

3. What are put options? 4

4. Buying and Selling of options 4

5. Premium of options 5

6. Valuation of options 5

7. Option prices 6

8. Benefits and risk of option trading 6

9. Reducing risk 7

10. Risking your principal 711. What is option moneyness? 8

12. Long call risk characteristics 9

13. Short call risk characteristics 10

14. Long put risk characteristics 11

15. Short put risk characteristics 12

16. Overview of Greeks 13

17. Delta basics 13

18. Gamma basics 15

19. Theta basics 1520. Vega basics 16

21. Rho basics 16

22. Conclusion 17

23. Bibliography 18

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What is an Option?

An option is a contract to buy or sell a specific financial product officially known as the option's

underlying instrument or underlying interest. For equity options, the underlying instrument is astock, exchange-traded fund (ETF), or similar product. The contract itself is very precise. Itestablishes a specific price, called the strike price, at which the contract may be exercised, oracted on. And it has an expiration date. When an option expires, it no longer has value and nolonger exists.

Options come in two varieties, calls and puts, and you can buy or sell either type. You makethose choices - whether to buy or sell and whether to choose a call or a put - based on what youwant to achieve as an options investor.

What Are Call Options?

A call option is a contractual agreement between a buyer and seller which gives the right, but notthe obligation, to the buyer to acquire a specified number of shares in a security at a predefinedprice (strike price) within a predefined amount of time. Each options contract represents 100shares in the underlying security; for example, 10 Apple July 09 $125 call options will allow theholder of the call option to purchase 1000 shares of Apple at $125 on or before optionsexpiration weekin July 2009.

Call options can be bought, sold, and even shorted. They are predominately used for purposes ofhedging but many traders will use them for speculative purposes as well. For example, the most

popular hedging strategy using calls is known as a covered call strategy. Traders will short callsto offset a portion of the downside risk of a stock that they own or lower the net cost ofpurchasing the stock. Conversely, a speculator may sell a call option without owningthe underlying security. This is known as a "naked" call and carries an unlimited risk.Remember, you are basically selling another trader the option to buy a stock at a certain price;therefore, the higher that the underlying moves, the more money you lose.

You can generally say that the price of a call option moves higher as the stock moves higher andvice versa. The risk of buying a call option is merely the amount of money that was paid for theoption. The upside profit potential of a long call option is unlimited.

Advantages of Call Options

Buying call options introduce two distinct advantages to a trader. First, they provide traders witha large amount of leverage. In our Apple example above, assume that the call was trading at$10. Therefore, the buyer would have to pay $10,000 ($10 * $120 * 10) to control 1000 sharesof Apple which currently trades at $120. You can see there is a 10 times leverage factor in this

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example. If Apple runs up to $140 and the call option is exercised, a $10,000 profit will berealized or 100%.

Secondly, as we have discussed above, call options allow traders to hedge their long positions,but not totally eliminate the risk.

Disadvantages of Call Options

The key disadvantage to buying call options is that it will expire worthless if you buy it and theunderlying security does not move higher. However, if you sell an option, this is exactly whatyou want to see happen. Additionally, in the wrong hands, options can be very dangerous.Some traders may speculate that the market is going to move lower and sell a boatload of callsonly to watch the stock move higher and put them on the hook for delivering the shares.

What are Put Options?

A put option is a contractual agreement between the buyer and the seller of the option that givesthe right, but not the obligation, for the put holder to force the seller of the put to purchase theunderlying security at the strike price on theoptions expiration date. The buyer of a putoption believes that the stock may move lower and therefore, decides to purchase the insuranceto protect the downside risk and thereby locks in a sales price if the stock moves lower. Seethe option risk profile of a put to understand the risks and rewards.

Puts may also be used for speculative purposes; if you short a put without it being a part of alarger strategy, this is called a "naked" put. The seller of a naked put is taking a bet that the stockwill move higher and that the premium that was received will expire worthless.

You can generally say that the price of a put option moves lower as the stock moves higher andvice versa. The risk of buying a put option is merely the amount of money that was paid for theoption. However, a put writer, or seller, has unlimited risk. The writer will be responsible forpurchasing the stock at a predefined price no matter how low the stock goes.

Buying and Selling of Options

If you buy a call, you have the right to buy the underlying instrument at the strike price on orbefore the expiration date. If you buy a put, you have the right to sell the underlying instrument

on or before expiration. In either case, as the option holder, you also have the right to sell the

option to another buyer during its term or to let it expire worthless.

The situation is different if you write, or "sell to open", an option. Selling to open a short option

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position obligates you, the writer, to fulfill your side of the contract if the holder wishes to

exercise. When you sell a call as an opening transaction, you're obligated to sell the underlying

interest at the strike price, if you're assigned. When you sell a put as an opening transaction,

you're obligated to buy the underlying interest, if assigned. As a writer, you have no control over

whether or not a contract is exercised, and you need to recognize that exercise is always possible

at any time until the expiration date. But just as the buyer can sell an option back into the market

rather than exercising it, as a writer you can purchase an offsetting contract, provided you have

not been assigned, and end your obligation to meet the terms of the contract. When offsetting a

short option position, you would enter a "buy to close" transaction.

Premium of Options

When you buy an option, the purchase price is called the premium. If you sell, the premium is

the amount you receive. The premium isn't fixed and changes constantly - so the premium you

pay today is likely to be higher or lower than the premium yesterday or tomorrow. What those

changing prices reflect is the give and take between what buyers are willing to pay and what

sellers are willing to accept for the option. The point at which there's agreement becomes the

price for that transaction, and then the process begins again.

If you buy options, you start out with what's known as a net debit. That means you've spent

money you might never recover if you don't sell your option at a profit or exercise it. And if you

do make money on a transaction, you must subtract the cost of the premium from any income

you realize to find your net profit.

As a seller, on the other hand, you begin with a net credit because you collect the premium. If the

option is never exercised, you keep the money. If the option is exercised, you still get to keep the

premium, but are obligated to buy or sell the underlying stock if you're assigned.

The Value of Options

What a particular options contract is worth to a buyer or seller is measured by how likely it is to

meet their expectations. In the language of options, that's determined by whether or not the

option is, or is likely to be, in-the-money or out-of-the-money at expiration. A call option is in-the-money if the current market value of the underlying stock is above the exercise price of the

option, and out-of-the-money if the stock is below the exercise price. A put option is in-the-

money if the current market value of the underlying stock is below the exercise price and out-of-

the-money if it is above it. If an option is not in-the-money at expiration, the option is assumed to

be worthless.

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An option's premium has two parts: an intrinsic value and a time value. Intrinsic value is the

amount by which the option is in-the-money. Time value is the difference between whatever the

intrinsic value is and what the premium is. The longer the amount of time for market conditions

to work to your benefit, the greater the time value.

Options Prices

Several factors, including supply and demand in the market where the option is traded, affect the

price of an option, as is the case with an individual stock. What's happening in the overall

investment markets and the economy at large are two of the broad influences. The identity of the

underlying instrument, how it traditionally behaves, and what it is doing at the moment are more

specific ones. Its volatility is also an important factor, as investors attempt to gauge how likely it

is that an option will move in-the-money.

Benefits and Risks of option trading

Most strategies that options investors use have limited risk but also limited profit potential. For

this reason, options strategies are not get-rich-quick schemes. Transactions generally require less

capital than equivalent stock transactions, and therefore return smaller dollar figures - but a

potentially greater percentage of the investment - than equivalent stock transactions.

Even those investors who use options in speculative strategies, such as writing uncovered calls,

don't usually realize dramatic returns. The potential profit is limited to the premium received forthe contract, and the potential loss is often unlimited. While leverage means the percentage

returns can be significant, here, too, the amount of cash changing hands is smaller than with

equivalent stock transactions.

Although options may not be appropriate for everyone, they're among the most flexible of

investment choices. Depending on the contract, options can protect or enhance the portfolios of

many different kinds of investors in rising, falling, and neutral markets.

Reducing Risk

For many investors, options are useful as tools of risk management, acting as insurance policies

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against a drop in stock prices. For example, if an investor is concerned that the price of his shares

in LMN Corporation is about to drop, he can purchase puts that give him the right to sell his

stock at the strike price, no matter how low the market price drops before expiration. At the cost

of the option's premium, the investor has insured himself against losses below the strike price.

This type of option practice is also known as hedging. While hedging with options may help you

manage risk, it's important to remember that all investments carry some risk, and returns are

never guaranteed. Investors who use options to manage risk look for ways to limit potential loss.

They may choose to purchase options, since loss is limited to the price paid for the premium. In

return, they gain the right to buy or sell the underlying security at an acceptable price for them.

They can also profit from a rise in the value of the option's premium, if they choose to sell it

back to the market rather than exercise it. Since writers of options are sometimes forced into

buying or selling stock at an unfavorable price, the risk associated with certain short positions

may be higher.

Many options strategies are designed to minimize risk by hedging existing portfolios. Whileoptions can act as safety nets, they're not risk free. Since transactions usually open and close in

the short term, gains can be realized very quickly. This means that losses can mount quickly as

well. It's important to understand all the risks associated with holding, writing, and trading

options before you include them in your investment portfolio.

Risking Your Principal

Like other securities - including stocks, bonds, and mutual funds - options carry no guarantees,

and you must be aware that it's possible to lose all of the principal you invest, and sometimesmore. As an options holder, you risk the entire amount of the premium you pay. But as an

options writer, you take on a much higher level of risk. For example, if you write an uncovered

call, you face unlimited potential loss, since there is no cap on how high a stock price can rise.

However, since initial options investments usually requires less capital than equivalent stock

positions, your potential cash losses as an options investor are usually smaller than if you'd

bought the underlying stock or sold the stock short. The exception to this general rule occurs

when you use options to provide leverage: Percentage returns are often high, but it's important to

remember that percentage losses can be high as well.

What is Option Moneyness?

You will hear the following terms when dealing with options: in the money, at the money, andout of the money. All three of these terms refer to the price of the options underlying securityrelative to the strike price of a specific option on that security.

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In the Money (ITM)

If the underlying security value is higher than the strike price of a call option, the option willhave intrinsic value and is said to be "In the Money", or ITM for short. Put options work theopposite way; if the underlying security is valued less than the strike price of the option, the

option is ITM. At expiration, the time value component of the option has completely decayed,leaving the option worth its intrinsic value.

To take this one step further, an option which is significantly in a profit position is consideredDeep in the Money. Deep in the money options are significantly in the money to the point wherethere is very little risk of them losing enough value to take them out of the money. For example,if the strike price of a call option is $15 and the stock is worth $25, we can call this deep in themoney. Deep in the money options also have a very high delta, close to 1, -1 for puts. High deltaindicates that the option will nearly move $1 for every $1 point move in the underlying.

Out of the Money (OTM)

For a call option, "Out of the Money" indicates that an options strike price is above the currentprice of the underlying security. If the option is out of the money, it has no intrinsic value and isonly worth the time premium. Again, the reverse can be said about put options; they are Out ofthe Money if the current price of the stock is above the strike price of the option.

Options in this category can also be classified as deep out of the money options as well. Deep outof the money call options have a strike price well above the current price of the security. Again,the odds of a deep out of the money option going into the money are very low and as such, thedelta is very low for these options. This means that the options will not move up as fast as thestock does in the case that the stock starts to rally.

At the Money (ATM)

"At the Money" refers to the underlying security having the same value, or one that is very closeto the options strike price and is also known as ATM.

LONG CALL RISK CHARACTERISTICS

Let's cover the risk profile of a call first. I believe examples in this section would be the bestway to cover this topic. We are going to start with a LONG CALL example.

Current Price of Stock $24.00

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Option Exercise Price $20.00

Call Premium $5.25

Months Till Expiration 3

In this scenario, we would be buying deep in the money callsfor $5.25, $4 in intrinsic value and$1.25 for 3 months of time premium. The buyer of this call optionis anticipating thatthe underlying security will be higher than $25.25 ($20 exercise or strike price + $5.25 optionpremium) within 3 months of time. Therefore, in our diagram below, thestrike priceis $20while the breakeven price is $25.25. As the stock moves above point b* or breakeven, the callbuyer is in a profit position. For example, assume the stock reaches $30 atexpiration; the callbuyer would be able to buy the stock at 10 point discount while only paying $5.25 forthat option.

Once the underlying security is above the strike price, the option will move penny for penny with

the security. The reward for the call buyer can be unlimited as the security can go as high as itwants to.

SHORT CALL RISK CHARACTERISTICS

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When someone is buying an option, there is obviously a seller on the other side who believes thatthe stock will not go above $25.25 within the next 3 months. Let's now take a look at the optionrisk profile of an option writer. For the sake of clarity, the term "write" refers to shorting orselling an option. Using the same example from above, the writer of the option has received apremium of $5.25 and will continue to remain in a profit position as long as the stock does not

move above $25.25.

Shorting an option brings added risk, especially if the seller is "naked". The term "naked option"refers to the idea that the seller of the stock does not own the underlying stock that mayeventually end up being called away by the purchaser of the option. Just like the nakedputoption, selling naked calls is a risky proposition and should be done only after much experiencesince there is no limit to the option based risk.

The most common use for selling a call is part of a common options strategy known asthe covered call. We will cover this strategy in far more detail, but the short story is that coveredcalls limit your downside exposure and add that extra bit of insurance and cushion to your long

position.

LONG PUT RISK CHARACTERISTICS

Lets start with a new example for the put section:

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Current Price of Stock $40.00

Option Exercise Price $40.00

Put Premium $5.00

Months Till Expiration 3

When initiating a long put option position, the option holder is looking to cover his/her downsiderisk in the event the stock takes a larger than expected hit. Puts allow the put buyers the abilityto force the writer of the option to buy the underlying stock at the strike price.

You may be asking what the difference between selling a call and buying a put is. They bothlimit your downside risk, right? Yes, but there are two key differences. Puts protect you againstdisastrous or rapid declines in a securities value; calls will only limit the downside up to thevalue of the premium you received for selling that call. The second key difference lies in the factthat selling a call results in a net debit to your account balance while buying a put will result in a

net credit, or a cash outlay.

By going long the put option for $5 with a strike price of $40, the breakeven price would be ($40+ $5), or $45. As the stock moves lower, the put buyer moves into a profit position, penny forpenny.

SHORT PUT RISK CHARACTERISTICS

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Finally, let's take a look at the short put risk chart. When you write a put option, or go short, youare selling premium in anticipation that the stock will move higher and therefore you will be ableto eat the entire option premium. Alternatively, a potential buyer of a stock may want to get longa stock and will sell puts to do it. Essentially, taking our example above, instead of buying thestock at $40 a share, the investor could short the put option for $5 and be forced to buy it at $40

if the stock moves lower at expiration. The bet here is that the stock wont drop below $35 ashare. If the stock moves above $40 at expiration, the writer of the option would have made $5per share as the option would never be exercised by the purchaser.

In our example below, the breakeven for this scenario would be ($40 - $5), or $35. As the stockmoves lower, the price of the put moves higher and this results in greater losses for the writer ofthe put.

OVERVIEW OF OPTION GREEKS

Option Greeks measure the options sensitivity to various risk components inherent to the price ofan option. These measures include the speed of the underlying securities price movement,interest rate movement, time decay of an option, and volatility.

Delta and Gamma measure the optionssensitivity to the speed of price changes in the underlyingsecurity, Rho measures the options interest rate sensitivity, Theta measures the change in the

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options price due to a change in the time left till expiration on the option, and Vega measures thechange in the options price due to changes in the options historical volatility.

DELTA BASICS

Delta measures the rate of change in the option price over the rate of change in the price of theunderlying security. Therefore, we can say that delta measures the speed of the option pricemovement relative to a single point move in the underlying security. Long callsand nakedputs have positive delta while shortcalls and longputshave negative delta.

Delta = (rate of change in option price) / (rate of change in underlying security price)

If you own a call option at $2 when the stock was $30 and now the stock moves up to $31 andthe option does as well to $2.50. In our formula above, the delta in this situation would be ($2.5 -$2) / ($31 - $30) = .5

Conversely, let's say you owned a put at $2.00 and the stock moved higher by one point whichresulted in the put option decreasing in value by $.5. The delta in this case would be ($1.5 - $2) /($31 - $30) = -.5

The closer the delta is to 1 or -1, the greater response in the price of the option when the price ofthe underlying changes.

The examples above assumed that nothing else changed; however, in reality, changes in vega,theta, and rho can impact delta.

Delta Ranges for Calls and Puts

If an option is in the money, the delta for a call will approach 1 while the delta of a put willapproach -1. At the money (ATM) options will be near .5 and -.5 while out of the money optionswill have a delta value approaching 0 as they move further out of the money. Also remember, asthe option comes closer to expiration, especially within 30 days, the delta curve becomes steeper;basically, the option becomes more sensitive to price movement in the underlying.

Delta Neutral Trading

Delta neutral trading, also known as "hedge" trading is a method of trading where the totalposition delta is 0. The idea is to hedge your position by slowing your position speed down.

Delta neutral trading is used by many traders to make profitable adjustments on their trade as theprice of the security moves up and down. For example, a popular strategy is to make adjustmentsto your total position to bring it back to delta neutral after the underlying security has moved20% in either direction. This can be done by making adjustments to the profitable side of yourtrade.

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Let's create a simple example of a delta neutral trade. Assume we bought 100 shares of Microsoftwhich would represent +100 deltas. We would need to either buy 2 at the money puts OR sell 2at the money calls OR buy 1 at the money put and sell 1 at the money call. Either scenario wouldget you to delta neutral.

Remember, delta neutral does NOT mean that you have set up a risk free position, it means thatyou have slowed down the speed of the percentage changes of your position.

GAMMA BASICS

The delta of a stock relies on the price of the stock in relation to thestrike price of the option.Therefore, when the stock price changes, so does the delta. This is where gamma becomesrelevant. Gamma is an estimation of the change in delta for a 1 point move in a stock and can be

thought of as the second derivative of delta. A large gamma value indicates that delta will shiftstrongly as the underlying security moves up and down.

A long call and long put will have positive gamma while the short counterparts will always benegative. A positive gamma refers to the idea that the delta of a long will become higher, orcloser to 1, as the underlying security moves higher. The long put gamma will also move closerto -1 as the underlying security continues to move lower. The opposite can be said for short callsand short puts.

Gamma reaches its highest value when a stock is trading at the money or near the money. Thisvalue goes lower and lower as the security moves further out of the money or furtherin the

money. This makes logical sense as the option price has the highest probability of moving frombeing OTM to ITM or ITM to OTM.

THETA BASICS

Theta represents the measure for time decay of an option. Remember, an option price consists ofintrinsic value and time premium. Theta measures the decay in time premium as every daypasses until options expiration. Therefore, we can say that the theta for a long call or put will benegative while the opposite can be said for the short call and put. This is true because when youare long an option, you will lose money in that option every day all else being equal due to thetime premium decaying. However, the time decay in a short option will increase your profits.

Theta does not adjust evenly as time goes on. The closer and closer the option is to expiration,the greater the time decay. Theta will accelerate at a higher rate especially when the option hasless than 30 days to go. This also makes logical sense since the option has less time to get or stayin a profitable situation. Additionally, an options theta will be highest when the stock is at the

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money. Since the stock has basically no intrinsic value, the time value component is the majorityof the premium and will fluctuate strongly as expiration approaches.

Relationship between Theta and Gamma

There is a direct correlation between theta and gamma. When an options gamma is high, thetheta moves higher as well. When we say higher, it means theta becomes more negative whichnegatively impacts the time premium for a long option holder. Some options traders will actuallyplay the high theta by selling shorter term options and buying that same strike option with agreater term to maturity at the same time. They are banking on the fact that the longer datedoption will have slower time decay than the shorter dated option.

VEGA BASICS

Moving on to the volatility component of an option; we measure the options price sensitivity tovolatility using Vega. Vega may also be referred to as kappa by some. Volatility can be

calculated by measuring the standard deviation of the last 30 days of closing prices in theunderlying security, commonly known as historical volatility. For example, if a $50 stock has a30% volatility figure, you can say that the expectation is for the stock trade between $35 and$65. Historical volatility is used to determine the fair value of the option; however, options rarelytrade in the open market at fair value. "Implied" volatility then estimates the volatility using themarket premium of the options. We do not want to go into too much detail on this but just knowthat there are two measurements for volatility and that one is derived from past market data andone is derived from current options premiums themselves.

We can go one step further to say that vega is a measurement of the change in the option pricefor each 1% adjustment in volatility. Using our example, if the vega for this option was 20, we

can say that the option would move higher by $1.00 if the stock's volatility

Higher volatility, or vega, results in higher option prices. This is true because higher volatilitygives the option a better chance to expire in the money.

Options exhibit the highest vega when the underlying is at the money and gradually declines asthe stock moves ITM or OTM.

RHO BASICS

Our last greek, Rho, measures theoretical option price changes due interest rate shifts. While this

measure of option price sensitivity is the least used, it has more relevant context when applied tohigher priced stocks. Why? Remember that a call option commands a large amount of stock witha relatively small amount of investment. Most times the value of the underlying that the optioncommands is worth in excess of 10 times the value of the option itself. If you would have to buythe stock, you would need quite a bit more money and the interest expense related that amount isbuilt into a call option premium. As you can see, as interest rates increase, a call option willincrease in value and a put option will decrease in value. It is for this reason that calls have a

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positive Rho when interest rates rise. Conversely, if interest rates fall, put premiums will increasewhile call premiums will decrease

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Conclusion:

Options are the opportunity provided by the seller of the option to the buyer of the option to buy

or sell the underlying asset at a specified price at a fixed date. The fixed date is known as expirydate and the specified price is known as strike price. In an option, the buyer has an option to buy

or sell the underlying asset, but not the obligation to do so, to the seller of the option.

The options are subjected to risk such as price movement, interest rate movement, time decay of

an option, and volatility this risk can be calculated by using the Greeks, i.e. Delta, Gamma,

Theta, Vega and Rho. These Greeks can be used to measure the risk of the option prices and help

in curbing the risks.

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Bibliography:

www.mysmp.com/options/

www.calloptionputoption.com

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http://www.mysmp.com/options/http://www.calloptionputoption.com/http://www.mysmp.com/options/http://www.calloptionputoption.com/

option and greeks (derivatives)

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