Options and Derivative Securities

Transcription

1 FIN 614 Options and Other Derivatives Professor Robert B.H. Hauswald Kogod School of Business, AU Options and Derivative Securities Derivative instruments can only exist in relation to some other financial instruments a security derived from underlying Usual four suspects from forward, to futures to swap the instrument apart: option Focus on the royal security: the holy grail options: fundamentals of options analysis and pricing extensions to corporate financial applications 4/5/2011 Introduction to Options - Robert B.H. Hauswald 2

2 In business? In football? In life? What is an Option? 4/5/2011 Introduction to Options - Robert B.H. Hauswald 3 A Taxonomy of Derivatives The foundation: forwards transact at a future date at a price specified today problem? The secure forward: futures contract exchange traded with settlement guarantee The repeated forward: FX, interest rate swap collection of forward contracts The anti-forward: financial options the right but not the obligation to transact in the future what has to be true about options? 4/5/2011 Introduction to Options - Robert B.H. Hauswald 4

3 Having the Cake and Eat It, too Options confer contractual rights on holder: a right to buy (sell) a fixed amount of an underlying asset at (over) a specified time (period) in the future at a price specified today Insurance vs. fixed commitment: right to buy or sell at discretion of holder wait and see security: even over time have an opinion while cutting off catastrophes Right means choice: choice means value value means what? 4/5/2011 Introduction to Options - Robert B.H. Hauswald 5 Two Types of Options An option gives the holder the right, but not the obligation, to buy or sell a given quantity of an asset on (or before) a given date, at prices agreed upon today. Calls versus Puts Call options gives the holder the right, but not the obligation, to buy a given quantity of some asset at some time in the future, at prices agreed upon today. When exercising a call option, you call in the asset. Put options gives the holder the right, but not the obligation, to sell a given quantity of an asset at some time in the future, at prices agreed upon today. When exercising a put, you put the asset to someone. 4/5/2011 Introduction to Options - Robert B.H. Hauswald 6

4 Option Jargon Exercising the Option act of buying or selling the underlying asset through the option contract. Strike Price or Exercise Price fixed price in the option contract at which the holder can buy or sell the underlying asset. Expiry: maturity date of the option is referred to as the expiration date, or the. European versus American options European options can be exercised only at. American options can be exercised at any time up to. 4/5/2011 Introduction to Options - Robert B.H. Hauswald 7 Options Contracts: Intrinsic Value In-the-Money The exercise price is less than the spot price of the underlying asset. At-the-Money The exercise price is equal to the spot price of the underlying asset. Out-of-the-Money The exercise price is more than the spot price of the underlying asset. Market jargon: money-ness 4/5/2011 Introduction to Options - Robert B.H. Hauswald 8

5 Option Theory: Building Blocks Options are priced relative to other assets their payoffs can be exactly replicated by a portfolio of risk free bonds and the underlying asset (e.g. stock) options can be priced by arbitrage methods! Options confer a right whose value depends on contingencies: use probability theory to evaluate them prerequisite: a model of the underlying asset s price distributional assumption: log-normal price changes Investors risk attitudes irrelevant for pricing options are priced relative to bonds and underlying their risk and expected return can be substantial 4/5/2011 Introduction to Options - Robert B.H. Hauswald 9 Value Components Intrinsic Value The difference between the exercise price of the option and the spot price of the underlying asset. Speculative Value The difference between the option premium and the intrinsic value of the option. Option Premium = Intrinsic Value + Speculative Value 4/5/2011 Introduction to Options - Robert B.H. Hauswald 10

6 Call Option Pricing at Expiry At, an American call option is worth the same as a European option with the same characteristics. If the call is in-the-money, it is worth: S T - E If the call is out-of-the-money, it is worthless: 0; hence, C at = C et = Max[S T - E, 0] Where S T is the value of the stock at (time T) E is the exercise price. C at is the value of an American call at C et is the value of a European call at 4/5/2011 Introduction to Options - Robert B.H. Hauswald 11 Long Call: Owning the Option 40 Buy a call Option payoffs ($) Stock price ($) Exercise price = $50 4/5/2011 Introduction to Options - Robert B.H. Hauswald 12

7 Short Call: Owing the Option 40 Option payoffs ($) Stock price ($) Write a call Exercise price = $50 4/5/2011 Introduction to Options - Robert B.H. Hauswald Call Option Profits Buy a call Option profits ($) Stock price ($) Write a call Exercise price = $50; option premium = $10 4/5/2011 Introduction to Options - Robert B.H. Hauswald 14

8 Option Payoffs: European Call Call: holder has choice (option) whether or not to buy in the future at strike price K, X, E at maturity T Hoder (buyer) pays the call price C t today to writer (seller): receives the option to buy in the future Call option payoffs: S T = Stock or asset price at T At Contract Date At Exercise Seller + C t - Max{ 0, S T - K } Buyer - C t + Max{ 0, S T - K } 4/5/2011 Introduction to Options - Robert B.H. Hauswald 15 Put Option Pricing at Expiry At, an American put option is worth the same as a European option with the same characteristics. If the put is in-the-money, it is worth E - S T. If the put is out-of-the-money, it is worthless: 0 P at = P et = Max[E - S T, 0] Notation as before with P denoting put value 4/5/2011 Introduction to Options - Robert B.H. Hauswald 16

9 Long Put: Holding the Option 40 Buy a put Option payoffs ($) Stock price ($) Exercise price = $50 4/5/2011 Introduction to Options - Robert B.H. Hauswald Short Put Sold the Option Option payoffs ($) Stock price ($) -40 write a put - Exercise price = $50 4/5/2011 Introduction to Options - Robert B.H. Hauswald 18

10 Option profits ($) Put Option Profits Write a put Buy a put Stock price ($) Exercise price = $50; option premium = $10 4/5/2011 Introduction to Options - Robert B.H. Hauswald 19 Option Payoffs: European Put Put: buyer has the choice (option) whether or not to sell at exercise price K, X, E at maturity T Buyer pays the put price (premium) P t today to the seller - receives the option to sell in the future Put option Payoffs: S T = Stock or asset price at T At Contract Date At Exercise Seller + P t - Max{ 0, K - S T } Buyer - P t + Max{ 0, K - S T } 4/5/2011 Introduction to Options - Robert B.H. Hauswald 20

11 Putting All together: Selling Options The seller (or writer) of an option has an obligation. The purchaser of an option has an option. Option profits Option ($) profits ($) Stock price ($) Buy a call Write a put Buy a put Write a call 100-4/5/2011 Introduction to Options - Robert B.H. Hauswald 21 Options Trading Most options traded OTC, some on exchanges Chicago Board Options Exchange stocks, stock market indices, treasury bonds Chicago Mercantile Exchange FX, interest rate, S&P and its subcomponents AMEX-Nasdaq stocks, stock market indices, oil and gas index, transportation index, treasury bills and notes Philadelphia Exchange stocks, foreign currencies, gold and silver indexes 4/5/2011 Introduction to Options - Robert B.H. Hauswald 22

12 Reading The Wall Street Journal --Call-- --Put-- Option/Strike Exp. Vol. Last Vol. Last IBM 130 Oct ¼ 107 5¼ 138¼ 130 Jan ½ 420 9¼ 138¼ 135 Jul ¾ /16 138¼ 135 Aug ¼ 94 5½ 138¼ 140 Jul ¾ 427 2¾ 138¼ 140 Aug ½ 58 7½ 4/5/2011 Introduction to Options - Robert B.H. Hauswald 23 Reading The Wall Street Journal This option has a strike price of $135; --Call-- --Put-- Option/Strike Exp. Vol. Last Vol. Last IBM 130 Oct ¼ 107 5¼ 138¼ 130 Jan ½ 420 9¼ 138¼ 135 Jul ¾ /16 138¼ 135 Aug ¼ 94 5½ 138¼ 140 Jul ¾ 427 2¾ 138¼ 140 Aug ½ 58 7½ a recent price for the stock is $ July is the expiration month 4/5/2011 Introduction to Options - Robert B.H. Hauswald 24

13 Reading The Wall Street Journal This makes a call option with this exercise price in-themoney by $3.25 = $138¼ $ Call-- --Put-- Option/Strike Exp. Vol. Last Vol. Last IBM 130 Oct ¼ 107 5¼ 138¼ 130 Jan ½ 420 9¼ 138¼ 135 Jul ¾ /16 138¼ 135 Aug ¼ 94 5½ 138¼ 140 Jul ¾ 427 2¾ 138¼ 140 Aug ½ 58 7½ Puts with this exercise price are out-of-the-money. 4/5/2011 Introduction to Options - Robert B.H. Hauswald 25 Reading The Wall Street Journal --Call-- --Put-- Option/Strike Exp. Vol. Last Vol. Last IBM 130 Oct ¼ 107 5¼ 138¼ 130 Jan ½ 420 9¼ 138¼ 135 Jul ¾ /16 138¼ 135 Aug ¼ 94 5½ 138¼ 140 Jul ¾ 427 2¾ 138¼ 140 Aug ½ 58 7½ On this day, 2,365 call options with this exercise price were traded. 4/5/2011 Introduction to Options - Robert B.H. Hauswald 26

14 Reading The Wall Street Journal The CALL option with a strike price of $135 is trading for $ Call-- --Put-- Option/Strike Exp. Vol. Last Vol. Last IBM 130 Oct ¼ 107 5¼ 138¼ 130 Jan ½ 420 9¼ 138¼ 135 Jul ¾ /16 138¼ 135 Aug ¼ 94 5½ 138¼ 140 Jul ¾ 427 2¾ 138¼ 140 Aug ½ 58 7½ Since the option is on 100 shares of stock, buying this option would cost $475 plus commissions. 4/5/2011 Introduction to Options - Robert B.H. Hauswald 27 Reading The Wall Street Journal --Call-- --Put-- Option/Strike Exp. Vol. Last Vol. Last IBM 130 Oct ¼ 107 5¼ 138¼ 130 Jan ½ 420 9¼ 138¼ 135 Jul ¾ /16 138¼ 135 Aug ¼ 94 5½ 138¼ 140 Jul ¾ 427 2¾ 138¼ 140 Aug ½ 58 7½ On this day, 2,431 put options with this exercise price were traded. 4/5/2011 Introduction to Options - Robert B.H. Hauswald 28

15 Reading The Wall Street Journal The PUT option with a strike price of $135 is trading for $ Call-- --Put-- Option/Strike Exp. Vol. Last Vol. Last IBM 130 Oct ¼ 107 5¼ 138¼ 130 Jan ½ 420 9¼ 138¼ 135 Jul ¾ /16 138¼ 135 Aug ¼ 94 5½ 138¼ 140 Jul ¾ 427 2¾ 138¼ 140 Aug ½ 58 7½ Since the option is on 100 shares of stock, buying this option would cost $81.25 plus commissions. 4/5/2011 Introduction to Options - Robert B.H. Hauswald 29 Option Value Determinants The value of a call option C 0 must fall within max (S 0 E, 0) < C 0 < S 0. The precise position will depend on these factors: Call Put 1. Stock price + 2. Exercise price + 3. Interest rate + 4. Volatility in the stock price Expiration date + + 4/5/2011 Introduction to Options - Robert B.H. Hauswald 30

16 Option payoffs ($) American and European Calls Profit 25 The value of a call option C 0 must fall within max (S 0 E, 0) < C 0 < S 0. Market Value S T Time value Intrinsic value Call loss E Out-of-the-money In-the-money 4/5/2011 Introduction to Options - Robert B.H. Hauswald 31 S T Options as Analytic Tools Options are part of larger group of instruments called contingent claims or derivative securities their value is contingent on underlying instrument common types: FX, interest and equity options (calls, puts), warrants, convertible debt option features are found in many corporate securities Option theory in corporate finance what is the value of defaulting on bonds? what is the value of convertible debt? risk and return for WACC convertible debt carries lower interest: is it cheaper? NO! 4/5/2011 Introduction to Options - Robert B.H. Hauswald 32

17 Summary and Outlook Introduction to option analysis jargon and payoffs put-call parity: absence of arbitrage Next big step: pricing calls and puts posit statistical model of return process use arbitrage ideas underlying PCP to find option prices: Black-Scholes-Merton framework Applications to corporate finance 4/5/2011 Introduction to Options - Robert B.H. Hauswald 33 Appendix: Common Strategies Portfolio insurance protective put Covered call counter-part to what put strategy? Long straddle long a call and put Short straddle short a call and put Long call spread 4/5/2011 Introduction to Options - Robert B.H. Hauswald 34

18 Long Put and Stock: Portfolio Insurance Value at Protective Put strategy has downside protection and upside potential $50 Buy the stock $0 $50 Buy a put with an exercise price of $50 Value of stock at 4/5/2011 Introduction to Options - Robert B.H. Hauswald 35 Protective Put Strategy Profits Value at $40 $0 -$40 Can you replicate this position? use T-bonds and calls $40 $50 Buy the stock at $40 Buy a put with exercise price of $50 for $10 Protective Put strategy has downside protection and upside potential Value of stock at 4/5/2011 Introduction to Options - Robert B.H. Hauswald 36

19 Value at $40 Covered Call Strategy Buy the stock at $40 $10 $0 -$30 -$40 $30 $40 $50 Sell a call with exercise price of $50 for $10 Covered call Value of stock at 4/5/2011 Introduction to Options - Robert B.H. Hauswald 37 Long Straddle: Buy a Call and a Put Value at $40 $30 Buy a call with an exercise price of $50 for $10 $0 -$10 -$20 $30 $40 $50 $ $70 Buy a put with an exercise price of $50 for $10 A Long Straddle only makes money if the stock price moves $20 away from $50. Value of stock at 4/5/2011 Introduction to Options - Robert B.H. Hauswald 38

20 Short Straddle: Sell a Call and a Put Value at $20 $10 $0 -$30 -$40 A Short Straddle only loses money if the stock price moves $20 away from $50. Sell a put with exercise price of $50 for $10 $30 $40 $50 $ $70 Sell a call with an exercise price of $50 for $10 Value of stock at 4/5/2011 Introduction to Options - Robert B.H. Hauswald 39 Value at Long Call Spread Buy a call with an exercise price of $50 for $10 $5 $0 -$5 -$10 $50 $55 $ long call spread Value of stock at Sell a call with exercise price of $55 for $5 4/5/2011 Introduction to Options - Robert B.H. Hauswald 40