Financial Derivative

FINANCIAL DERIVATIVES :FINANCIAL DERIVATIVES Sukumar Nandi Indian Institute of Management Lucknow


The Major Issues :The Major Issues What is Risk? Three important players: Hedger, speculator, Arbitreguer. functions performed by derivative markets. (a) Price Discovery (b) Risk transfer © Market competition What are derivatives ? Forward contract Problem Futures Hedging using futures Contract Valuation of Futures Option : Call option & Put option Different terminologies Examples of Call option Examples of Put option Hedging with option Factors affecting option price Valuation of option Black and scholes model


Slide 3 :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 Forward Future Option Swap 1. Forward Contract A 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 sellers Buyer Seller Money Security Who takes a long position Who takes a short position


Slide 4 :Problems of Forwards Counter - 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


Slide 5 :Future Contracts A future contract is a standerized forward contract between two parties where one of the parties commits to sell and the other to buy a stipulated quantility 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 Future Price = Spot price + carry costs - carry return


Futures v/s Forwards :Futures v/s Forwards Exchange traded & transparent v/s Private contracts Standardised v/s Customised Settlement through Clearing House v/s Settlement between Buyers and Sellers Require margin payment v/s no margins Mark - to - Market margins v/s no margins Counter - 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.


Slide 7 :Futures Individual stock Future Index futures Underlying asset is the individual stock Underlying asset is the stock index BSE Sensex Future S & P Nifty Future one lot= 200 indices One lot = 50 indices BSE SENSEX? 30 shares S & P Nifty? 50 shares


Slide 8 :Future Price Spot price 4568 4535 4500 4590 4570 4600 4700 Future Price= Spot price Op. CL. 1 CL.2 CL.3 CL.4 CL.27 Jan. -1650 + 2750 - 1000 + 1500 Future Price of January Index Future (maturing on 27th Jan. last Thursday)


Slide 9 :Margin Money Margin Money @ 5%= Rs. 4568x50x 5/100= Rs.228400 x 5/100=Rs.11420 Marking to Market 1st day when price decreases from Rs. 4568 to Rs.4535 loss per index = Rs. 33 (4568 - 4535) Total loss= Rs. 50 X 33= 1650 2nd day Gain (4590 - 4535) X 50 = 55 X 50 = 2750 3rd day Loss (4590 - 4570) X 50 = 20 X 50 = 1000 4th day Gain (4600 - 4570) X 50 = 30 X 50 = 1500 Margin (at the beginning)= Rs. 11420 Total gain upto 4th day 1st day Less: Loss 1650 (4600 - 4568) x 50 = 32 x 50 = 1600 2nd day Add: Gain 2750 i.e. 13020 - 11420 = 1600 3rd day Loss : Loss 1000 4th day Add : 1500= 13020


How to protect your portfolio :How to protect your portfolio What can go wrong in times of volatility - panic selling What 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 ? :How ? 22nd January, 2008 Raju has a portfolio of 5 securities worth Rs. 1,87,085 - The beta of the portfolio is 0.95 Hence he needs to sell index futures worth 0.95*187085 = Rs. 1,77,731 i.e. 1 market lot The expiry date of Nifty Jan. futures is 27th Feb, 2008 Sell Nifty futures at 1141 10 Feb, 2003 Nifty July futures trading at 970.60 Portfolio value reduced to Rs. 1,54,095 Raju 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


Slide 12 :Valuation of Futures Prices Price = Spot Price + Carry Costs - Carry Return Case 1 : Securities Providing No Income F = Soe rt. Where F = Future price S = Spot Price r = the risk free rate of interest p.a. with continuous compounding t = the time to murturity e = exponential value = 2.7183 Example: Consider a forward contract on a non-dividend paying share which is available at Rs. 70, to mature in 3 - months’ time r = .08 (Compounded continuously) (.08) (.25) F = So e rt = Rs. 70 e(.08) (.25) = Rs. 70 e .02 = Rs. 70 (1.0202)= Rs. 71.41


Slide 13 :Case 2 : Securities Providing a known cash Income F = (S - I) e rt. I = PV of Income D received after t time. I = De-rt Example : Let us consider a 6- month future contract on 100 shares with a price of Rs. 38 each. The risk free rate of interest (continuously compounded) is 10% p.a. The share in question is expected to yield a dividend of Rs. 1.50 in 4 months from now. What is F ? Div. Receivable after 4 months = 100 X 1.50 = 150 P.V. of the div; I = 150 e-(0.1)(4/12) = 150 x 0.9672 = Rs. 145.08 F = (3800 - 145.08) e (0.1) (0.5) = 3654.92 X 1.05127 = Rs. 3842.31


Slide 14 :Case 3 : Securities Providing a Known Yield F = S e (r - y) t y = Yield rate (continuously compounded) Example : Assume that the stocks underlying an index provide a dividend yield of 4% p.a., the current value of the index is Rs. 520 and that the continuously compounded risk free rate of interest is 10% p.a. Here S = 520, r = 0.10, y = 0.09, t= 3/12 = 0.25 Thus : F = 520 e (0.1 - 0.04) (0.25) = 520 e (0.06) (0.25) = 520 x 1.0151 = Rs. 527.85


Slide 15 :OPTION An 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 Option Call option Put option Option 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


Slide 16 :Exercise Price : the price at which the contract is settled (strike price) Expiration date : the date on which the option expires. Style of option American option European option Exercised at any time prior to expiration Exercised on the expiration date Option Premium : The price that the holder of on option pays and the writer of on option received for the rights conveyed by the option.


Slide 17 :Option on individual stock Call Option : X = option writer (Seller) Y = option buyer (holder) Size of the contract = 100 R.I. Shares Spot price on 22.01.2003 = Rs. 40 per share Exercise price = Rs. 42 per share Date of maturity = 21.03.2003 Option price = Re 1 per share for call option Profit/ Loss Profile for seller & buyer Possible spot price at call maturity X (Rs.) Y (Rs.) 40 100 (100 X 1) - 100 41 100 (100 X 1) - 100 42 100 (100 X 1) - 100 BEP 43 0 0 44 - 100 (100 X 1) 100 45 - 200 (100 X 2) 200 46 - 300 (100 X 3) 300


Slide 18 :Profit 300 200 100 0 -100 -200 -300 Share Price 40 41 42 43 44 45 46 (a) For Call option writer X


Slide 19 :Profit 300 200 100 0 100 200 300 Share Price 40 41 42 43 44 45 46 (b) For Call option buyer


Slide 20 :Example of Put option : X = Option writer => obligation to buy Y = Option buyer => right to sell Exercise 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 share Profit/ Loss Profile for X and Y Possible sport price (Rs.) X Y 60 -3000 (100 X 30) 3000 70 -2000 (100 X 20) 2000 80 -1000 (100 X 10) 1000 BEP --> 90 0 0 100 1000 -1000 110 1000 -1000 120 1000 -1000


Slide 21 :Profit 3000 2000 1000 -1000 -2000 -3000 Share Price 60 70 80 90 100 110 120 (a) Option writer (X)


Slide 22 :Profit 3000 2000 1000 -1000 -2000 -3000 Share Price 60 70 80 90 100 110 120 (b) Option buyer (Y)


Slide 23 :Have a view on the market ? A. Assumption : Bullish on the market over the short term: Action : Buy Nifty Calls Example : 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. 1470 Option Value : = Rs. 40 (1470 - 1430) Less : option Premium = 20 Profit per Nifty: 20 Profit on the contract = 20 X 200 = 4000


Slide 24 :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 = 23 Profit per Nifty = 17 Profit on the contract = Rs. 3400 (17 X 200)


Slide 25 :Use Put as a portfolio hedge ? To protect your portfolio from possible market crash. Possible Action : Buy Nifty Puts You held a portfolio valued at Rs. 10 lakhs Portfolio Beta = 1.13 Current Nifty = 1440 Strike price = 1420 Premium = Rs. 26 To hedge, you bought 4 puts [800 Nifty, equivalent to Rs. (10 X 1.13) lakhs or 11,30,000] If at expiration Nifty declines to 1329 and your portfolio falls to Rs. 948276, then Option Value = 91 (1420 - 1329) Option premium = 26 Profit per Nifty = 65 Profit on the contract = Rs. 52000 (65 X 800) Loss on Portfolios = Rs. 51724 Net Profit = Rs. 276


Slide 26 :SPREADS A spread trading strategy involves taking a position in two or more options of the same type. Bull Spreads A bull spread reflects the bullish sentiment of a trader. It can be created by taking the following position: Expiry Exer. Price Option Premium 1. Buy a Call option Same E1 P1 2. Sell a Call option Same E2 P2 P1 >P2 E1 Premium Received (P2) Cash outflow for option premium = P1 - P2 If P1 = 8, P2 = 2. Cash outflow = Rs. (8 - 2) = Rs. 6 i.e. initial cost of the spread Let E1 = 30, E2 = 50.


Slide 27 :Possible spot Price on Expiry If S1= 20 If S1=40 If S1= 60 (1) (2) (3) Rs. 10 Rs. 10 Rs. 10 Rs. 10 20 20 (S1) 20 20 30 30 (E1) 30 (E1) 30 (E1) 40 40 40 (S1) 40 50 50 (E2) 50 (E2) 50 (E2) 60 60 60 60 (S1) 70 70 70 70 Pay offer from a Bull spread (Using Call) Price of Store Pay off from Pay off from Total Long term Short term Pay off (1) S1E2 S1 - E1 E2 - S1 E2 - E1 (60-30) (50-60) (50-30=20)


Slide 28 :Bear Spread In Contract 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. It can be created by taking the following position: Expiry Exer. Price O. Premium 1. Buy a Call Same E1 P1 2. Sell a Call Same E2 P2 E1>E2 P1

Slide 29 :Possible spot Price on Expiry If S1= 20 If S1=40 If S1= 60 (1) (2) (3) Rs. 10 Rs. 10 Rs. 10 Rs. 10 20 20 (S1) 20 20 30 (E2) 30 (E2) 30 (E2) 30 (E2) 40 40 40 (S1) 40 50 (E1) 50 (E1) 50 (E1) 50 (E1) 60 60 60 60 (S1) 70 70 70 70 Pay offer from a Bull spread (Using Call) Price of Store Pay off from Pay off from Total Long term Short term Pay off (1) S1S1 S1 - E1 E2 - S1 E2 - E1 (60-50) (30-60) (30-50= -20) E2

Slide 30 :Butterfly Spreads. The strategy is obviously meant for on investor who feels that large price changes are unlike;y 1. Buy a Call E1 2. Buy end the call E3 3. Sell 2 Calls E2 E1

Slide 31 :Possible spot Price on Expiry If S1= 20 If S1=35 If S1= 45 If S1=60 (1) (2) (3) (4) Rs. 10 Rs. 10 Rs. 10 Rs. 10 Rs. 10 20 20 (S1) 20 20 20 30 (E1) 30 (E1) 30 (E1) 30 (E1) 30(E1) 40(E2) 40 (E2) 40 (E1) 40 (E2) 40(E2) 50 (E3) 50 (E3) 50 (E3) 50 (E3) 50(E3) 60 60 60 60 60(S1) 70 70 70 70 70 Price Stock Pay off from Pay off from Pay off from Total Ist long call (E1) 2nd long cells(E3) short call (E3) Pay off (1) S1E3 S1 - E1 0----- 2( E2 - S1) E3 - S1 E1S1

Factors Affecting Call option Premium :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).


Slide 33 :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 = 42 33 34 35 36 37 38 39 40 41 42 43 44 45 46 If E = 42 option is exercised when S is greater than or equal to 43 If S = 40, E = 37 i.e. S>E lower E compared to S, higher is the probability to exercise the option => higher option price.


Slide 34 :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 option 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 S> E If E1 = 39, S = 40 Option will be exercised when price is les than or equal to 39 If S= 40 E2 = 45 S < E S is relatively low, the higher the probability to exercise the option. High option premium


Slide 35 :The Black and Scholes Model (1973) C = S0 N (d1) - E e -rt. N (d2) Where d1 = log (S0 / E) + (r + 0.5σ 2) t σ ( t ) 1/2 d2 = log (S0 / E) + (r - 0.5 σ 2) t σ ( t ) 1/2 C = Current value of the option r = Continuously compounded riskless rate of returns S0 = Current price of stock E = Exercise Price T = time remaining before the expiration date (expressed as a fraction of a year) σ = S.D. of continuously compounded annual rate of return Log= Natural togarithen N(d) = value of the commulative normal distribution evaluated at d


Slide 36 :Example : Consider the following information with regard to call option on the stock of X Ltd., S0 = Rs. 120 E = Rs. 115 Time period = 3 months; thus t = 0.25 year σ = 0.6 r = 0.10 d1 = log (120/115) + (0.10 + 0.5 X 0.6 2).25 0.6 V 0.25 = 0.37 d2 = log (120/115) + (0.10 - 0.5 X 0.6 2 ) X .25 0.6 V 0.25 =0.07 .1443 d1 =20.37 .0279 d2 = 0.07 N (d1) = 0.6443 N (d2) = 0.5279


Slide 37 :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) = 18.11 Using 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


Slide 38 :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 S0 Determination of TERMINAL Values of Portfolios Portfolio Cash Flow at t = 0 S1> E S1≤ E P1 C S1 - E 0 E e -rt. E E Total S1 E P2 P 0 E - S1 S0 S1 S1 Total S1 E Since 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 + S0 or P = C + E e - rt.. - S0


Slide 39 :SWAP A SWAP transaction is one where two or more parties exchange (SWAP) one set of predetermined payments for another. (i) Interest rate SWAP (ii) Currency SWAP Interest Rate SWAP. Company Fixed (%) Floating (%) A 7.5 M IBOR + 0.5% B 9 M IBOR + 3.5% A borrows Rs. 10,000 from a bank at Floating rate B borrows Rs. 10,000 from a bank at Fixed rate As 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%


Slide 40 :SWAP A B (7%) (LIBOR + 0.5%) To understand the benefits from the swap consider the net cash flows of A and B Party Swap Swap Swap outflows on Total loan from bank (%) A - 7 (MIBOR + 0.5%) -(MIBOR + 0.5%) - 7 B - (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 LIBOR + 2.5% (this is better the LIBOR + 3.5%) (B gain 1%) (A gains 0.5%)


Slide 41 :Presence of a Broker C As 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 LIBOR + 0.5%. (iii) B will pay C a floating rate of LIBOR + 0.5% (iv) B will receive from C a fixed rate of 6.5% SWAP LIBOR + 0.5 A C LIBOR + 0.5% B 7% 6.5% C gains (7% - 6.5%) = 0.5%


Slide 42 :To understand the benefits from the Swap consider the net cash flows of A, B, and C Party Swap Swap Outflows Total Outflow (%) inflows (%) on loan A - 7.0 + (L + 0.5) - (L + o.5) - 7.0 B - (L+0.5) + 6.5 - 9 - (L + 3) L + 0.5 L + 0.5 C - + Nil + 0.5 + 6.5 + 7 It 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 (LIBOR+ 3%) which is better than (LIBOR + 3.5%). [B gains 0.5%] (c) for C, a profit of 0.5% for earning the transaction.