Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 1 Chapter 16 Options Markets

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 2 Option Terminology Buy - Long Sell - Short Call Put Key Elements –Exercise or Strike Price –Premium or Price –Maturity or Expiration

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 3 Market and Exercise Price Relationships In the Money - exercise of the option would be profitable Call: market price>exercise price Put: exercise price>market price Out of the Money - exercise of the option would not be profitable Call: market price>exercise price Put: exercise price>market price At the Money - exercise price and asset price are equal

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 4 American vs European Options American - the option can be exercised at any time before expiration or maturity European - the option can only be exercised on the expiration or maturity date

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 5 Different Types of Options Stock Options Index Options Futures Options Foreign Currency Options Interest Rate Options

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 6 Payoffs and Profits on Options at Expiration - Calls Notation Stock Price = S T Exercise Price = X Payoff to Call Holder ( S T - X) if S T >X 0if S T < X Profit to Call Holder Payoff - Purchase Price

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 7 Payoffs and Profits on Options at Expiration - Calls Payoff to Call Writer - ( S T - X) if S T >X 0if S T < X Profit to Call Writer Payoff + Premium

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 8 Profit Stock Price 0 Call Writer Call Holder Profit Profiles for Calls

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 9 Payoffs and Profits at Expiration - Puts Payoffs to Put Holder 0if S T > X (X - S T ) if S T < X Profit to Put Holder Payoff - Premium

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 10 Payoffs and Profits at Expiration - Puts Payoffs to Put Writer 0if S T > X -(X - S T )if S T < X Profits to Put Writer Payoff + Premium

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 11 Profit Profiles for Puts 0 Profits Stock Price Put Writer Put Holder

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 12 Equity, Options & Leveraged Equity - Text Example InvestmentStrategyInvestment Equity onlyBuy shares$8,000 Options onlyBuy options$8,000 LeveragedBuy options $1,000 equityBuy 2% $7,000 Yield

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 13 Equity, Options & Leveraged Equity - Payoffs Microsoft Stock Price $75$80$100 All Stock$7,500$8,000$10,000 All Options$0$0$16,000 Lev Equity $7,140$7,140 $9,140

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 14 Equity, Options & Leveraged Equity - Rates of Return Microsoft Stock Price $75 $80$100 $75 $80$100 All Stock-6.25% 0% 25% All Options-100% -100%100% Lev Equity % %14.25%

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 15 Put-Call Parity Relationship S T X Payoff for Call Owned 0S T - X Payoff for Put Written-( X -S T ) 0 Total Payoff S T - X S T - X

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 16 Payoff of Long Call & Short Put Long Call Short Put Payoff Stock Price Combined = Leveraged Equity

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 17 Arbitrage & Put Call Parity Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal. C - P = S 0 - X / (1 + r f ) T If the prices are not equal arbitrage will be possible

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 18 Put Call Parity - Disequilibrium Example Stock Price = 110 Call Price = 17 Put Price = 5 Risk Free = 10.25% Maturity =.5 yr X = 105 C - P > S 0 - X / (1 + r f ) T > (105/1.05) 12 > 10 Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 19 Put-Call Parity Arbitrage ImmediateCashflow in Six Months PositionCashflowS T 105 Buy Stock-110 S T S T Borrow X/(1+r) T = Sell Call+17 0-(S T -105) Buy Put S T 0 Total 2 0 0

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 20 Option Strategies Protective Put Long Stock Long Put Covered Call Long Stock Short Call Straddle (Same Exercise Price) Long Call Long Put

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 21 Option Strategies Spreads - A combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration Vertical or money spread Same maturity Different exercise price Horizontal or time spread Different maturity dates

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 22 Exotic Options Asian Options Barrier Options Lookback Options Currency-Translated Options Binary Options

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 23 Chapter 17 Option Valuation

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 24 Option Values Intrinsic value - profit that could be made if the option was immediately exercised –Call: stock price - exercise price –Put: exercise price - stock price Time value - the difference between the option price and the intrinsic value

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 25 Time Value of Options: Call Option value X Stock Price Value of Call Intrinsic Value Time value

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 26 Factors Influencing Option Values: Calls FactorEffect on value Stock price increases Exercise price decreases Volatility of stock price increases Time to expirationincreases Interest rate increases Dividend Ratedecreases

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 27 Binomial Option Pricing: Text Example Stock Price C 75 0 Call Option Value X = 125

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 28 Binomial Option Pricing: Text Example Alternative Portfolio Buy 1 share of stock at $100 Borrow $46.30 (8% Rate) Net outlay $53.70 Payoff Value of Stock Repay loan Net Payoff Payoff Structure is exactly 2 times the Call

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 29 Binomial Option Pricing: Text Example C C = $53.70 C = $26.85

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 30 Another View of Replication of Payoffs and Option Values Alternative Portfolio - one share of stock and 2 calls written (X = 125) Portfolio is perfectly hedged Stock Value50200 Call Obligation Net payoff50 50 Hence C = or C = 26.85

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 31 Black-Scholes Option Valuation C o = S o e -  T N(d 1 ) - Xe -rT N(d 2 ) d 1 = [ln(S o /X) + (r –  +  2 /2)T] / (  T 1/2 ) d 2 = d 1 - (  T 1/2 ) where C o = Current call option value. S o = Current stock price N(d) = probability that a random draw from a normal dist. will be less than d.

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 32 Black-Scholes Option Valuation X = Exercise price.  = Annual dividend yield of underlying stock e = , the base of the nat. log. r = Risk-free interest rate (annualizes continuously compounded with the same maturity as the option. T = time to maturity of the option in years. ln = Natural log function  Standard deviation of annualized cont. compounded rate of return on the stock

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 33 Call Option Example S o = 100X = 95 r =.10T =.25 (quarter)  =.50  = 0 d 1 = [ln(100/95)+(.10-0+(  5 2 /2))]/(  5 .25 1/2 ) =.43 d 2 =.43 - ((  5 .25 1/2 ) =.18

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 34 Probabilities from Normal Dist. N (.43) =.6664 Table 17.2 d N(d) Interpolation

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 35 Probabilities from Normal Dist. N (.18) =.5714 Table 17.2 d N(d)

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 36 Call Option Value C o = S o e -  T N(d 1 ) - Xe -rT N(d 2 ) C o = 100 X e -.10 X.25 X.5714 C o = Implied Volatility Using Black-Scholes and the actual price of the option, solve for volatility. Is the implied volatility consistent with the stock?

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 37 Put Option Value: Black-Scholes P=Xe -rT [1-N(d 2 )] - S 0 e -  T [1-N(d 1 )] Using the sample data P = $95e (-.10X.25) ( ) - $100 ( ) P = $6.35

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 38 Put Option Valuation: Using Put-Call Parity P = C + PV (X) - S o = C + Xe -rT - S o Using the example data C = 13.70X = 95S = 100 r =.10T =.25 P = e -.10 X P = 6.35

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 39 Using the Black-Scholes Formula Hedging: Hedge ratio or delta The number of stocks required to hedge against the price risk of holding one option Call = N (d 1 ) Put = N (d 1 ) - 1 Option Elasticity Percentage change in the option’s value given a 1% change in the value of the underlying stock

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 40 Portfolio Insurance - Protecting Against Declines in Stock Value Buying Puts - results in downside protection with unlimited upside potential Limitations –Tracking errors if indexes are used for the puts –Maturity of puts may be too short –Hedge ratios or deltas change as stock values change