FINANCIAL DERIVATIVESWhat is Risk? Three important players: Hedger, Speculator, Arbitrageur.Functions performed by derivative markets. (a) Price discovery, (b) Risk transfer, (C) Market completion What are derivatives ? Forward contract Futures Option : Call option & Put option SWAP

What are derivatives?A derivative instrument, broadly, is a financial contract whose pay off structure is determined by the value of an underlying commodity, security, interests rate, share price index, exchange rate, oil price etc.A derivative instrument derives its value from some underlying variables.Financial Derivatives

ForwardFutureOptionSwap

1. Forward ContractA forward contract is a simple derivative that involves an agreement to buy/sell an asset on a certain date at an agreed price. This is a contract between two parties: Buyers and sellersBuyerSellerMoney

Security Who takes a long positionWho takes a short position

Problems of ForwardsCounter - party risk:A party to the contract may not fulfil the obligation. Thus each party faces the risk of default.

Low degree of liquidity: Both the parties have to wait till maturity. No one can come out from the contract.

Future ContractsA future contract is a standardized forward contract between two parties where one of the parties commits to sell and the other to buy a stipulated quantity of a security or an index at an agreed price on or before a given date in the future.

Seller A(Buyer)Buyer B (Seller)Clearing House

Futures v/s Forwards Exchange traded & transparent v/s Private contractsStandardised v/s Customised Settlement through Clearing House v/s Settlement between Buyers and SellersRequire margin payment v/s no marginsMark - to - Market margins v/s no marginsCounter - party risk is absent in Futures (settlement of trades is guaranteed)Most settled by offset and very few by delivery v/s most settled by actual delivery.

FuturesIndividual stock futureIndex futuresUnderlying asset is the individual stockUnderlying asset is the stock indexBSE Sensex FutureS & P Nifty Future one lot= 200 indices One lot = 50 indicesBSE SENSEX? 30 sharesS & P Nifty? 50 shares

Future PriceSpot price4568453545004590457046004700Future Price= Spot priceOp. CL. 1CL.2CL.3CL.4CL.27 Jan.-1650 + 2750 - 1000 + 1500Future Price of January Index Future (maturing on 27th Jan. last Thursday)

Margin MoneyMargin Money @ 5%= Rs. 4568x50x 5/100= Rs.228400 x 5/100=Rs.11420Marking to Market1st day when price decreases from Rs. 4568 to Rs.4535 loss per index = Rs. 33 (4568 - 4535) Total loss= Rs. 50 X 33= 16502nd day Gain (4590 - 4535) X 50 = 55 X 50 = 27503rd day Loss (4590 - 4570) X 50 = 20 X 50 = 10004th day Gain (4600 - 4570) X 50 = 30 X 50 = 1500Margin (at the beginning)= Rs. 11420 Total gain upto 4th day1st day Less: Loss - 1650 (4600 - 4568) x 50 = 32 x 50 = 16002nd day Add: Gain + 2750 i.e. 13020 - 11420 = 1600 3rd day Loss : Loss - 1000 4th day Add : Gain + 1500= 13020

How to protect your portfolio from market crashWhat can go wrong in times of volatility - panic sellingWhat can be done- Hedge long position on the portfolio, with short position on Nifty futures- Beta of the portfolio = weighted average of betas of individual stocks

How ?5th March 2015Raju has a portfolio of 5 securities worth Rs. 1,87,085 - The beta of the portfolio is 0.95Hence he needs to sell index futures worth 0.95*187085 = Rs. 1,77,731 i.e. 1 market lotThe expiry date of Nifty March futures is 27th March 2015Sell Nifty futures at 114119 March 2015 Nifty March futures trading at 970.60Portfolio value reduces to Rs. 1,54,095Raju unwound the position making a profit of Rs. 1090. i.e. portfolio dropped by Rs. 32990 and his sell position on Nifty gained by Rs.34080

OPTIONAn option is a contract which gives the right, but not the obligation, to buy or sell the underlying at a stated date and at a stated price.Underlying assets Indices

S & P CNX Nifty (introduced on 4.6.2001 in NSE)Individual Stock(Introduced on 2.7.2001

OptionCall optionPut optionOption Type Buyer of option Seller of option (option holder) (option writer) (a) Call Right to buy obligation to sell (b) Put Right to sell obligation to buy

Exercise Price : the price at which the contract is settled (strike price)Expiration date : the date on which the option expires. Style of optionAmerican optionEuropean option Exercised at any time prior to expirationExercised on the expiration dateOption Premium :The price that the holder of an option pays and the writer of an option received for the rights conveyed by the option.

Option on individual stockCall Option : X = option writer (Seller)Y = option buyer (holder)Size of the contract = 100 R.I. Shares Spot price on today= Rs. 40 per shareExercise price = Rs. 42 per shareDate of maturity = after one mothOption price = Re 1 per share for call optionProfit/ Loss Profile for seller & buyerPossible spot price at call maturity X (Rs.)Y (Rs.) 40100 (100 X 1)- 100 41100 (100 X 1)- 100 42100 (100 X 1)- 100BEP 43 0 0 44- 100 (100 X 1) 100 45- 200 (100 X 2) 200 46- 300 (100 X 3) 300

Profit

300200100 0-100-200-300Share Price 40 41 42 43 44 45 46(a) For Call option writer X

Profit

300200100 0100200300Share Price40 41 42 43 44 45 46(b) For Call option buyer

Example of Put option :X = Option writer =>obligation to buyY = Option buyer => right to sellExercise price = Rs. 100 per ACC share; size of the contract = 100 ACC shares, spot price today = Rs. 105 per share ;option premium = Rs. 10 per shareProfit/ Loss Profile for X and YPossible sport price (Rs.)XY60-3000 (100 X 30)3000 70 -2000 (100 X 20) 2000 80 -1000 (100 X 10) 1000BEP --> 90 0 0 100 1000 -1000 110 1000 -1000 120 1000 -1000

Profit

300020001000 -1000-2000-3000Share Price 60 70 80 90 100 110 120 (a) Option writer (X)

Profit

300020001000 -1000-2000-3000Share Price 60 70 80 90 100 110 120 (b) Option buyer (Y)

Have a view on the market ?A. Assumption : Bullish on the market over the short term: Action : Buy Nifty CallsExample : Current Nifty is Rs. 1400 Buy one Nifty. The strike price 1430 Option premium = Rs. 20 Total premium = Rs. (20 X 200) = Rs. 4000 If at expiration Nifty advances by 5% i.e. 1470Option Value : = Rs. 40 (1470 - 1430)Less : option Premium = 20Profit per Nifty: 20Profit on the contract = 20 X 200 = 4000

B. Assumption : Bearish on the market over the short term. Possible Action : Buy Nifty Put Example : Nifty in cash market is Rs. 1400. Buy one contract of Nifty puts for Rs. 23 each. The strike price is 1370 if at expiration Nifty declines by 5% i.e. Rs. 1330.Option Value = 40 (1370 - 1330)Option Premium = 23Profit per Nifty = 17Profit on the contract = Rs. 3400 (17 X 200)

Factors Affecting Call option Premium (i)Level of existing spot price relative to strike price (exchange price) S>E, the higher will be the option premium.(ii) Length of time before the expiration date.(iii) Potential variability of stock Price The greater the Variability, the higher the P (S>E).

Call Option. (right to buy)* Level of Existing Spot Price (s) relative to Exercise Price (E).The higher the spot rate (S) relative to exercise price (E), the higher the option price.If S>E, higher option price, higher probability of exercise of option.If S = 40, E = 423334353637383940414243444546

If E = 42 option is exercised when S is greater than or equal to 43If S = 40, E = 37 i.e. S>E lower E compared to S, higher is the probability to exercise the option=> higher option price.

Put Option (right to Sell)The lower the spot rate (s) relative to exercise price (E), the higher the option price. Relating S>E, the higher probability to exercise the option333435363738394041424344454647S> E If E1 = 39, S = 40Option will be exercised when price is les than or equal to 39 If S= 40E2 = 45S < E S is relatively low, the higher the probability to exercise the option.High option premium

The Black and Scholes Model (1973) C = S0 N (d1) - E e -rt. N (d2)Where d1 = log (S0 / E) + (r + 0.5 2) t ( t )1/2d2 = log (S0 / E) + (r - 0.5 2) t ( t )1/2C = Current value of the option r = Continuously compounded riskless rate of returns S0 = Current price of stockE = Exercise Pricet = time remaining before the expiration date (expressed as a fraction of a year) = S.D. of continuously compounded annual rate of returnLog= Natural logarithm N(d) = value of the commulative normal distribution evaluated at d

Example :Consider the following information with regard to call option on the stock of X Ltd.,S0 = Rs. 120E = Rs. 115Time period = 3 months; thus t = 0.25 year = 0.6r = 0.10 d1 = log (120/115) + (0.10 + 0.5 X 0.6 2).250.6 (0.25)1/2 = 0.37d2 = log (120/115) + (0.10 - 0.5 X 0.6 2 ) X .250.6 (0.25)1/2=0.07 .1443d1 =0.37 .0279d2 = 0.07N (d1) = 0.6443N (d2) = 0.5279

The value of the Call is C = S0 N (d1) - E e -rt. N (d2) = 120 X (0.6443) - 115 e -0.10 (.25) X (0.5279) = 18.11Using the put- call parity, we can determine the put option value on the share as follows:P = C + E e -rt. -S0 = 18.11 + 115 X e - 0.10 (0.25) - 120 = Rs. 10.27

Relationship between European Call and put options:Portfolio P1:One European call option & cash for an amount of E e -rt..Portfolio P2:One European put option & one share of stock worth S0Determination of TERMINAL Values of PortfoliosPortfolio Cash Flow at t = 0S1> E S1 EP1 C S1 - E 0E e -rt. E ETotal S1 EP2P 0 E - S1 S0 S1 S1Total S1 ESince both the portfolios have identical values on expiration, they must have equal values at present as well. Accordingly we have C + E e - rt.. = P + S0or P = C + E e - rt.. - S0

SWAPA SWAP transaction is one where two or more parties exchange (SWAP) one set of predetermined payments for another.Interest Rate SWAP.CompanyFixed (%)Floating (%)A7.5M IBOR + 0.5%B9M IBOR + 3.5%A borrows Rs. 10,000 from a bank at Floating rateB borrows Rs. 10,000 from a bank at Fixed rateAs a separate transaction A and B agree as follows:(i) A will pay B a fixed rate of 7%(ii) B will pay A a floating rate of MIBOR + 0.5%

SWAPAB(7%)(MIBOR + 0.5%)To understand the benefits from the swap consider the net cash flows of A and BPartySwap Swap Outflows on Bank Loan TotalA- 7 (MIBOR + 0.5%)-(MIBOR + 0.5%)- 7B - (MIBOR + 0.5%)+ 7%- 9% - (MIBOR+2.5)Outflow (%)Inflow(%)It may be seen that the net result is (a)For A, a fixed rate obligation at 7% (this is better than the 7.5% which A would have paid if it had directly taken a fixed rate loan). (b)For B, a floating rate obligation at MIBOR + 2.5% (this is better then MIBOR + 3.5%)(B gains 1%)(A gains 0.5%)

Presence of a Broker CAs a separate transaction A,B, and C agree as follows:(i) A will pay C a fixed rate of 7%(ii) A will receive from C a floating rate of MIBOR + 0.5%.(iii) B will pay C a floating rate of MIBOR + 0.5%(iv) B will receive from C a fixed rate of 6.5%SWAPMIBOR + 0.5ACMIBOR + 0.5%B7%6.5%C gains (7% - 6.5%) = 0.5%

To understand the benefits from the Swap consider the net cash flows of A, B, and CPartySwapSwapOutflowsTotalOutflow (%)inflows (%)on loanA- 7.0+ (M + 0.5)- (M + o.5)- 7.0B- (M+0.5)+ 6.5- 9- (M + 3) M + 0.5 M + 0.5C-+ Nil + 0.5 + 6.5 + 7It may be seen that the net result is(a) for A, fixed rate obligation at 7% (this is better than the 7.5%[A gains 0.5% (7.5 - 7)](b) for B, a floating rate obligation at (MIBOR+ 3%) which is betterthan (MIBOR + 3.5%). [B gains 0.5%](c) for C, a profit of 0.5% for earning the transaction.

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