Essentials of Investments: Chapter 15 - Options Markets Option Terminology, Market and Exercise Price Relationships, American vs European Options, Different Types of Options, Payoffs and Profits on Options at Expiration - Calls.
1 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Chapter 15 Options Markets Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved Bodie • Kane • Marcus Essentials of Investments Fourth Edition Option Terminology • • • • • Buy - Long Sell - Short Call Put Key Elements – Exercise or Strike Price – Premium or Price – Maturity or Expiration Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved Bodie • Kane • Marcus Essentials of Investments Fourth Edition Different Types of Options • • • • • Stock Options Index Options Futures Options Foreign Currency Options Interest Rate Options Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved Bodie • Kane • Marcus Essentials of Investments Fourth Edition Payoffs and Profits on Options at Expiration - Calls Notation Stock Price = ST Exercise Price = X Payoff to Call Holder (ST - X) if ST >X if ST < X Profit to Call Holder Payoff - Purchase Price Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved Bodie • Kane • Marcus Essentials of Investments Fourth Edition Payoffs and Profits on Options at Expiration - Calls Payoff to Call Writer - (ST - X) if ST >X if ST < X Profit to Call Writer Payoff + Premium Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved Bodie • Kane • Marcus Essentials of Investments Fourth Edition Profit Profiles for Calls Profit Call Holder Call Writer Stock Price Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved Bodie • Kane • Marcus Essentials of Investments Fourth Edition Payoffs and Profits at Expiration Puts Payoffs to Put Holder if ST > X (X - ST) if ST < X Profit to Put Holder Payoff - Premium Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 10 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Payoffs and Profits at Expiration Puts Payoffs to Put Writer if ST > X -(X - ST) if ST < X Profits to Put Writer Payoff + Premium Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 26 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Factors Influencing Option Values: Calls Factor Effect on value Stock price increases Exercise price decreases Volatility of stock price increases Time to expiration increases Interest rate increases Dividend Rate decreases Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 27 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Binomial Option Pricing: Text Example 200 100 75 C 50 Stock Price Irwin / McGraw-Hill Call Option Value X = 125 © 2001 The McGraw-Hill Companies, Inc All rights reserved 28 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Binomial Option Pricing: Text Example Alternative Portfolio Buy share of stock at $100 Borrow $46.30 (8% Rate) 53.70 Net outlay $53.70 Payoff Value of Stock 50 200 Repay loan - 50 -50 Net Payoff 150 Irwin / McGraw-Hill 150 Payoff Structure is exactly times the Call © 2001 The McGraw-Hill Companies, Inc All rights reserved 29 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Binomial Option Pricing: Text Example 150 53.70 75 C 0 2C = $53.70 C = $26.85 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 30 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Another View of Replication of Payoffs and Option Values Alternative Portfolio - one share of stock and calls written (X = 125) Portfolio is perfectly hedged Stock Value 50 200 Call Obligation -150 Net payoff 50 50 Hence 100 - 2C = 46.30 or C = 26.85 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 31 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Black-Scholes Option Valuation Co = Soe-dTN(d1) - Xe-rTN(d2) d1 = [ln(So/X) + (r – d + s2/2)T] / (s T1/2) d2 = d1 - (s T1/2) where Co = Current call option value So = Current stock price N(d) = probability that a random draw from a normal dist will be less than d Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 32 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Black-Scholes Option Valuation X = Exercise price d = Annual dividend yield of underlying stock e = 2.71828, 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 s = Standard deviation of annualized cont compounded rate of return on the stock Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 33 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Call Option Example So = 100 X = 95 r = 10 T = 25 (quarter) s = 50 d = d1 = [ln(100/95)+(.10-0+(.5 2/2))]/(.5 251/2) = 43 d2 = 43 - ((.5)( 251/2) = 18 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 34 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Probabilities from Normal Dist N (.43) = 6664 Table 17.2 d N(d) 42 6628 43 6664 Interpolation 44 6700 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 35 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Probabilities from Normal Dist N (.18) = 5714 Table 17.2 d N(d) 16 5636 18 5714 20 5793 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 36 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Call Option Value Co = Soe-dTN(d1) - Xe-rTN(d2) Co = 100 X 6664 - 95 e- 10 X 25 X 5714 Co = 13.70 Implied Volatility Using Black-Scholes and the actual price of the option, solve for volatility Is the implied volatility consistent with the stock? Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 37 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Put Option Value: Black-Scholes P=Xe-rT [1-N(d2)] - S0e-dT [1-N(d1)] Using the sample data P = $95e(-.10X.25)(1-.5714) - $100 (1-.6664) P = $6.35 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 38 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Put Option Valuation: Using Put-Call Parity P = C + PV (X) - So = C + Xe-rT - So Using the example data C = 13.70 X = 95 S = 100 r = 10 T = 25 P = 13.70 + 95 e -.10 X 25 - 100 P = 6.35 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 39 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 (d1) Put = N (d1) - Option Elasticity Percentage change in the option’s value given a 1% change in the value of the underlying stock Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 40 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved ... Essentials of Investments Fourth Edition Put-Call Parity Relationship ST < X ST > X ST - X Payoff for Call Owned Payoff for Put Written-( X -ST) Total Payoff Irwin / McGraw-Hill ST - X ST - X © 2001... Marcus Essentials of Investments Fourth Edition Payoffs and Profits at Expiration Puts Payoffs to Put Writer if ST > X -( X - ST) if ST < X Profits to Put Writer Payoff + Premium Irwin / McGraw-Hill... Stock -6 .25% 0% 25% All Options -1 00% -1 00% 100% Lev Equity -1 0.75% -1 0.75% 14.25% Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 15 Bodie • Kane • Marcus Essentials