...Synthetic Forward and PutCallParity A synthetic long forward can be created by purchasing a call option and writing a put option with the same strike price and the same expiration date. Let’s say, that an investor buys a $500‐strike call option and sells a $500‐strike put option, both options have the same expiration time T. At T, the spot price will be equal to, above or below the strike price. If the spot price is above the strike price K, the investor will exercise the call option and buy the underlier for $500. The put will not be exercised. If the spot price is below the strike price the written put will be exercised against the investor, forcing him to buy the underlier at $500. The call will expire worthless. In either case, the underlier will be purchased at the strike price. The payoff of this combined position is max{0, S - K}- max{0, K - S} = S - K Call Put but this is actually the payoff of a long forward contract expiring at time T and with a forward price of $500. Be aware of the differences between an original long forward and a synthetic long forward: (i) the original long forward has no upfront premium payment while the synthetic long forward requires a net option premium (= abs[Call(K,T) – Put(K,T)] ) as upfront payment. (ii) At expiration at time T we pay the forward price with the original long forward, whereas with the synthetic long forward we pay the strike price. Let F0,T denote the “no‐arbitrage” forward price. This means you have to pay $0 today and at ...
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...FDRM Project On 9/17/2014 Estimation of NIFTY Spot Price Using Put-Call Parity Under the guidance of Professor Rajiv Srivastava Submitted by: Abhay Sharma (1A) Ayush Gupta (9C) Sachin Gupta (38A) Shikhar Mathur (45A) Table of Contents 1. 2. 3. 4. 5. 6. Executive Summary………….………………………..……………………………….………………..2 Introduction ……………………..………………………………………………………………….……..3 1.1 Why Derivative Markets…………………………….………………………………………………….……..3 1.2 Derivative Markets………………………………………………………………………………………….……3 1.3 Types of Traders……………………………………………………………………………………………………5 1.4 Types of Contracts………………………………………………………………………………………………..5 1.5 Development of Indian Derivatives Market…………………………………………………………..6 Objectives of the Study……………………………………………………….………………………..6 Research Methodology ………………………………………………………………………………..7 Properties of Data…………………………………………………………………………………………7 4.1 Analysis of different contracts…..………………………………………………………………………….9 4.2 Comparison between Call and Put Trade Volume ….……………………………………..……10 4.3 Speculation ratio…………………………………………………………………………………………………11 4.4 Estimation of NIFTY spot Price using Put-Call Parity……………………………………………13 Conclusion………………………………………………………………………………………………….15 Appendix…………………………………………………………………………………………………….16 1 Executive Summary Futures and options markets in India are relatively new. The National Stock Exchange (NSE) introduced trading in Index Options (also based on Nifty) on June 4, 2001. The Futures and Options on...
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...BUSINESS INTELLIGENCE USING SAS PROJECT ON “PUT CALL PARITY ON NIFTY INTRADAY DATA” AT INSTITUTE OF MANAGEMENT TECHNOLOGY, HYDERABAD BY ADITI GUPTA SHIWANI SHARMA SWATI TOMAR TULIKA CHAMADIA APPROVED BY DR. CHAKRAPANI (ASSOCIATE PROFESSOR) DATE OF SUBMISSION 15th October, 2013 ACKNOWLEDGMENT We would like to thank several people for their support and encouragement during the project without which this project would not have been a success. At first, we would like to extend my thanks to our Project Mentor/Guide Dr. Chakrapani, Associate Professor at Institute of Management Technology, Hyderabad, who gave us such a nice subject and project to work on which helped us to get the insight on the subject. Apart from this he always helped and guided us at every point of time of the project. He has been a continuous guide for putting in the correct efforts as well as how to improvise on the quality in time. He has been a great support in bringing this project to the desired format. At last we would also like to extend a special thanks to the other project members, friends and family who always supported us throughout the project. Table of Contents ACKNOWLEDGMENT 2 1. INTRODUCTION 4 OPTION CONTRACT 4 TYPES OF OPTION CONTRACT 4 OPTION PRICING 4 INTEREST RATES AND DIVIDENDS 5 PUT-CALL PARITY 6 2. PUT-CALL PARITY INTRADAY ON INDEX DATA 6 OBJECTIVE 6 METHODOLOGY 6 FINDINGS 7 CONCLUSION: 9 PROGRAM: 9 1. INTRODUCTION OPTION...
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...Copyright © 2009 by National Stock Exchange of India Ltd. (NSE) Exchange Plaza, Bandra Kurla Complex, Bandra (East), Mumbai 400 051 INDIA All content included in this book, such as text, graphics, logos, images, data compilation etc. are the property of NSE. This book or any part thereof should not be copied, reproduced, duplicated, sold, resold or exploited for any commercial purposes. Furthermore, the book in its entirety or any part cannot be stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise. Preface The National Stock Exchange of India Ltd. (NSE), set up in the year 1993, is today the largest stock exchange in India and a preferred exchange for trading in equity, debt and derivatives instruments by investors. NSE has set up a sophisticated electronic trading, clearing and settlement platform and its infrastructure serves as a role model for the securities industry. The standards set by NSE in terms of market practices; products and technology have become industry benchmarks and are being replicated by many other market participants. NSE has four broad segments Wholesale Debt Market Segment (commenced in June 1994), Capital Market Segment (commenced in November 1994) Futures and Options Segment (commenced June 2000) and the Currency Derivatives segment (commenced in August 2008). Various products which are traded on the NSE include, equity shares, bonds, debentures, warrants, exchange...
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...Copyright © 2009 by National Stock Exchange of India Ltd. (NSE) Exchange Plaza, Bandra Kurla Complex, Bandra (East), Mumbai 400 051 INDIA All content included in this book, such as text, graphics, logos, images, data compilation etc. are the property of NSE. This book or any part thereof should not be copied, reproduced, duplicated, sold, resold or exploited for any commercial purposes. Furthermore, the book in its entirety or any part cannot be stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise. Preface The National Stock Exchange of India Ltd. (NSE), set up in the year 1993, is today the largest stock exchange in India and a preferred exchange for trading in equity, debt and derivatives instruments by investors. NSE has set up a sophisticated electronic trading, clearing and settlement platform and its infrastructure serves as a role model for the securities industry. The standards set by NSE in terms of market practices; products and technology have become industry benchmarks and are being replicated by many other market participants. NSE has four broad segments Wholesale Debt Market Segment (commenced in June 1994), Capital Market Segment (commenced in November 1994) Futures and Options Segment (commenced June 2000) and the Currency Derivatives segment (commenced in August 2008). Various products which are traded on the NSE include, equity shares, bonds, debentures, warrants, exchange...
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...10.2. What is a lower bound for the price of a four-month call option on a non-dividend-paying stock when the stock price is $28, the strike price is $25, and the risk-free interest rate is 8% per annum? The lower bound is [pic] Problem 10.3. What is a lower bound for the price of a one-month European put option on a non-dividend-paying stock when the stock price is $12, the strike price is $15, and the risk-free interest rate is 6% per annum? The lower bound is [pic] Problem 10.4. Give two reasons that the early exercise of an American call option on a non-dividend-paying stock is not optimal. The first reason should involve the time value of money. The second reason should apply even if interest rates are zero. Delaying exercise delays the payment of the strike price. This means that the option holder is able to earn interest on the strike price for a longer period of time. Delaying exercise also provides insurance against the stock price falling below the strike price by the expiration date. Assume that the option holder has an amount of cash [pic] and that interest rates are zero. When the option is exercised early it is worth [pic] at expiration. Delaying exercise means that it will be worth [pic] at expiration. Problem 10.5. “The early exercise of an American put is a trade-off between the time value of money and the insurance value of a put." Explain this statement. An American put when held in conjunction with the underlying stock provides...
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... Review of Option Types • A call is an option to buy • A put is an option to sell • A European option can be exercised only at the end of its life • An American option can be exercised at any time 2 Derivatives - Options Give the holder the right to buy or sell the underlying at a certain date for a certain price. (European options) • • • • • Right to buy call option Right to sell put option Payoff function: call: C(T)= max{S(T)-K, 0}, put: P(T)=max{K-S(T),0} Cash settlement Exchanges: CBOE, CBOT, Eurex, LIFFE, ... Derivatives - Options • • • • Strike K Maturity T Buy option Sell option you can buy or sell for that price date when the option expires long position (holder) short position (writer) Exercising ... ... only at maturity possible European ... at any date up to maturity possible American Option Positions • • • • Long call Long put Short call Short put 5 Long Call (Figure 9.1, Page 195) Profit from buying one European call option: option price = $5, strike price = $100, option life = 2 months 30 Profit ($) 20 10 70 0 -5 loss 80 90 100 Terminal stock price ($) 110 120 130 6 Short Call (Figure 9.3, page 197) Profit from writing (selling) one European call option: option price = $5, strike price = $100 Profit ($) 5 0 -10 -20 110 120 130 70 80 90 100 Terminal stock price ($) -30 7 Long Put (Figure 9.2, page 196) Profit from buying a European put option: option price = $7, strike...
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...Sensitivities and Option Hedging Answers to Questions and Problems 1. Consider Call A, with: X $70; r 0.06; T t 90 days; DELTA, GAMMA, THETA, VEGA, and RHO for this call. c DELTA GAMMA THETA VEGA RHO $1.82 .2735 .0279 8.9173 9.9144 3.5985 0.4; and S $60. Compute the price, 0.4; and S $60. Compute the price, 2. Consider Put A, with: X $70; r 0.06; T t 90 days; DELTA, GAMMA, THETA, VEGA, and RHO for this put. p DELTA GAMMA THETA VEGA RHO $10.79 .7265 .0279 4.7790 9.9144 13.4083 3. Consider a straddle comprised of Call A and Put A. Compute the price, DELTA, GAMMA, THETA, VEGA, and RHO for this straddle. price DELTA GAMMA THETA VEGA RHO c p $12.61 0.2735 0.7265 0.4530 0.0279 0.0279 0.0558 8.9173 4.47790 13.6963 9.9144 9.9144 19.8288 3.5985 13.4083 9.8098 119 120 CHAPTER 14 OPTION SENSITIVITIES AND OPTION HEDGING 4. Consider Call A. Assuming the current stock price is $60, create a DELTA-neutral portfolio consisting of a short position of one call and the necessary number of shares. What is the value of this portfolio for a sudden change in the stock price to $55 or $65? As we saw for this call, DELTA 0.2735 shares 1 call, costs: 0.2735. The DELTA-neutral portfolio, given a short call component, is .2735 ($60) $1.82 $14.59 If the stock price goes to $55, the call price is $.77, and the portfolio will be worth: .2735 ($55) $.77 $14.27 With a stock price of $65, the call is worth $3.55, and the portfolio value is: .2735 ($65) $3.55 $14.23 Notice that...
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...-10000 - 2500 2500 7500 15000 Payoff from Call Brought 10000 5000 Bank NIfty 0 8400 8500 8600 8700 8800 8900 9000 9100 9200 9300 9400 9500 9600 9700 -5000 -10000 -15000 -20000 9800 Bullish on Bank Nifty Example: Sell 1 Call Option* Bank Nifty 8900 8800 25 400 8400 Profit, when: Bank Nifty does not go down and option expires unexercised Loss, when: Bank Nifty goes down and option exercised Bank Nifty 10000 10000 10000 10000 10000 10000 8000 8200 8400 8600 8800 9000 -20000 -15000 -10000 -5000 0 0 10000 5000 0 5000 10000 10000 15000 Payoff from Put Sold 10000 5000 Bank NIfty 0 8000 8100 8200 8300 8400 8500 8600 8700 8800 8900 9000 -5000 -10000 -15000 -20000 9100 Bank Nifty ITM Call Strike Price 25 Call Premium OTM Call Strike Price Call Premium Break Even Pay-off from ITM Call brought Pay-off from OTM Call Sold 8900 8700 500 9000 400 8900 Bank Nifty 8500 8200 8400 8600 8800 -12500 -12500 -10000 -5000 0 10000 10000 10000 7500 2500 -2500 -2500 0 2500 2500 15000 10000 5000 0 8200 8300 8400 8500 8600 8700 8800 8900 9000 9100 Payoff from Call Brought Payoff from Call Sold Net Payoff Bank NIfty 9200 9300 9400 9500 9600 -5000 -10000 -15000 -20000 Example: Buy 1 ITM Call Option and Sell 1 OTM Call Option* Bank Nifty Sell OTM Put Strike Price 25 Put Premium Buy OTM Put Call Strike Price Put Premium Break Even Pay-off from Put sold Pay-off from Put purchase 8900 8800 500 8500 400 9000 Bank...
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...Chapter 12 & 20 Chapter 21 The Black-Scholes Formula and Option Greeks Adapted from Black & Scholes (1973), The Pricing of Options and Corporate Liabilities, The Journal of Political Economy, Vol. 81, No. 3., pp. 637-654. 2 Black-Scholes Assumptions • Assumptions about stock return distribution Continuously compounded returns on the stock are normally distributed and there is no jumps in the stock price The volatility is a known constant Future dividends are known, either as discrete dollar amount or as a fixed dividend yield • Assumptions about the economic environment The risk-free rate is a known constant There are no transaction costs or taxes It is possible to short-sell costlessly and to borrow at the risk-free rate 3 Black-Scholes Assumptions • The original paper by Black and Scholes begins by assuming that the price of the underlying asset follows a process like the following dS (t ) ( )dt dZ (t ) S (t ) where (20. 1) S(t) is the stock price dS(t) is the instantaneous change in the stock price is the continuously compounded expected return on the stock δ is the dividend yield on the stock is the continuously compounded standard deviation (volatility) Z(t) is the standard Brownian motion dZ(t) is the change in Z(t) over a short period of time 4 Black-Scholes Assumptions • There are 2 important implications of equation (20.1) Suppose the stock price now is S(0). If the stock...
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...spot market, and for speculating on subsequent spot movements. › Hedging - Fiduciary call writing - Covered call writing - Protective put buying › Synthetic futures contracts › Speculating - Spreads - Straddles - other 2 › Fiduciary call writing - Writing call options against an asset already held - Involves frequent rebalancing to maintain a hedged position › Covered call writing - Hedger simply writes one call option for each unit of asset held › Synthetic puts - Created by one call option for each unit of an asset sold short › Protective put buying - Purchase of put options to insure a long asset position › Synthetic call - The combination of a short asset and a written put 3 Creating Synthetic Futures Contracts › Options can be combined to create synthetic futures contracts › A combination of options that consists of a written European call and a purchased european put, with the same exercise prices and expirations, behaves in a manner identical to a short position in a futures contract. › A long position in a synthetic futures contract is created by purchasing European calls and writing corresponding puts. 4 Put-call futures parity › A riskless portfolio consisting of short futures contract and long synthetic futures contract Position Current Value STX Short Futures 0 Tf0 Long Call CE 0 ST-X Short Put -PE -(X-ST) 0 Tf0 Tf0 CE -PE - ST –X Tf0 - ST –X ...
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...investment strategies: 1. Buying the stock (LONG STOCK): is when we buy a stock of AT&T with a Spot Price(So) of $55 in time zero (t=0) with the expectation that the asset will rise in value. Profit is equal to Stock Price minus the Spot Price. If the Stock Price is greater than the Spot Price we will have a profit, and if the Stock Price is less than the Spot Price we will have a loss. Page 5: 2. Buying a call option (LONG CALL): A call option is a contract in which the buyer has the right ,but not the obligation to buy 100 shares of AT&T at a specified price(Strike Price of $55 within a fixed period of time until its expiration in 4 days, at call premium of (c) $0.5. Profit is equal to Stock Price minus the strike price minus the call premium. In order to use this strategy, the investing firm must be expecting that the Stock Price will increase in the future. By exercising the call option, the company will buy the stock at the strike price and sell it for St in the market. Page 6: 3. Writing a Call option (SHORT CALL): A call option is a...
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...in 67 days, we must use 68 days since that is the option's time to expiration. 2. (Minimum Value of a Call) This would create an arbitrage opportunity. The call would be purchased and immediately exercised. For example, suppose S0 = 44, X = 40, and the call price is $3. Then an investor would buy the call and immediately exercise it. This would cost $3 for the call and $40 for the stock. Then the stock would be immediately sold for $44, netting a risk-free profit of $1. In other words, the investor could obtain a $44 stock for $43. Since everyone would do this, it would drive the price of the call up to at least $4. If the call were European, however, immediate exercise would not be possible (unless, of course, it was the expiration day), so the European call could technically sell for less than the intrinsic value of the American call. We saw, though, that the European call has a lower bound of the stock price minus the present value of the exercise price (assuming no dividends). Since this is greater than the intrinsic value, the European call would sell for more than the intrinsic value. Then at expiration, it would sell for the intrinsic value. 3. (Lower Bound of a European Call) The call is underpriced, so buy the call, sell short the stock, and buy risk-free bonds with face value of X. The cash received from the stock is greater than the cost of the call and bonds. Thus, there is a positive cash flow up front. The payoffs from the portfolio at expiration...
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...Xiaolin Li, Shengyu Zhang, Riley David and Strick Jacob QUESTION 1 #1: Buying Calls * If ST < $55, we won’t exercise the call, and lose the premium of$2.875; * If ST > $55, we will exercise the call and the net profit will be ST - $55 - $2.875 = ST - $57.875 #2: Writing Calls * If ST < $55, the call buyer will not exercise the call, thus we earn the premium of $2.875; * If ST > $55, the call buyer will exercise the call and our net profit is $2.875 + $55 – ST = $57.875 - ST #3: Buying Puts * When ST > $55, we won’t exercise the put and will lose the premium of $2.625; * When ST < $55, we begin to earn money ($55 - ST – $2.625) #4: Writing Puts * When ST > $55, keep our premium of $2.625; * When ST < $55, need to purchase the stock, payoff is ST - $55 + 2.625 QUESTION 2 • Which one of the strategies offers the greatest upside return? Buying calls since it can provide infinite profit as stock price grows. • Which one of the strategies offers the least upside returns? Writing puts because the most you can earn is your premium and premium of puts is lower than that of calls. • Which one of the strategies offers the greatest downside potential? Writing calls since when stock price reaches really high, your potential loss is infinite. • Which one of the strategies offers the least downside potential? Buying puts because the most you can lose is...
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...CHAPTER 7: ADVANCED OPTION STRATEGIES END-OF-CHAPTER QUESTIONS AND PROBLEMS 1. (Bull Spread) Buy one put with exercise price X1 and sell one put with exercise price X2. The profit equation is ( = Max(0, X1 – ST) – P1 – Max(0, X2 – ST) + P2 If ST < X1 < X2 ( = X1 – ST – P1 – X2 + ST + P2 = X1 – X2 – (P1 – P2) Recall from Chapter 3 that the difference between exercise prices is less than the difference between premiums. Since X1 < X2 and P1 < P2, the above profit is negative. If X1 < ST < X2 ( = – P1 – X2 + ST + P2 This figure increases dollar for dollar with ST. The breakeven is found by setting the profit to zero, – P1 – X2 + ST* + P2 = 0 and solving for ST* ST* = X2 + (P1 – P2) If X1 < X2 ( ST ( = – P1 + P2 Since P2 > P1, this figure is positive. The minimum profit occurs in the first profit range, ST < X1 < X2 and equals X1 – X2 – (P1 – P2). The maximum profit occurs in the third profit range, X1 < X2 < ST and equals – P1 + P2. 2. (Straddle) A straddle is a strategy based on the expectation that the market will have high volatility. If, however, everyone else in the market believes that the market will have high volatility, then the prices of the call and put will reflect the higher volatility, which will result in breakeven points further away from the current stock price. A straddle is most likely to be successful when the investor believes that the market will be more volatile...
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