Bài giảng Essentials of Investments - Chapter 15 Options Markets

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus1 Chapter 15 Options Markets Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus2 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 • Marcus3 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 • Marcus4 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 • Marcus5 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 • Marcus6 Payoffs and Profits on Options at Expiration - Calls Notation Stock Price = ST Exercise Price = X Payoff to Call Holder (ST - X) if ST >X 0 if ST < 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 • Marcus7 Payoffs and Profits on Options at Expiration - Calls Payoff to Call Writer - (ST - X) if ST >X 0 if ST < 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 • Marcus8 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 • Marcus9 Payoffs and Profits at Expiration - Puts Payoffs to Put Holder 0 if ST > X (X - ST) if ST < 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 • Marcus10 Payoffs and Profits at Expiration - Puts Payoffs to Put Writer 0 if ST > X -(X - ST) if ST < 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 • Marcus11 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 • Marcus12 Equity, Options & Leveraged Equity - Text Example Investment Strategy Investment Equity only Buy stock @ 80 100 shares $8,000 Options only Buy calls @ 10 800 options $8,000 Leveraged Buy calls @ 10 100 options $1,000 equity Buy T-bills @ 2% $7,000 Yield Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus13 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 • Marcus14 Equity, Options & Leveraged Equity - Rates of Return Microsoft Stock Price $75 $80 $100 All Stock -6.25% 0% 25% All Options -100% -100% 100% Lev Equity -10.75% -10.75% 14.25% Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus15 Put-Call Parity Relationship ST X Payoff for Call Owned 0 ST - X Payoff for Put Written-( X -ST) 0 Total Payoff ST - X ST - X Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus16 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 • Marcus17 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 = S0 - X / (1 + rf) 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 • Marcus18 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 > S0 - X / (1 + rf) T 17- 5 > 110 - (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 • Marcus19 Put-Call Parity Arbitrage Immediate Cashflow in Six Months Position Cashflow ST 105 Buy Stock -110 ST ST Borrow X/(1+r)T = 100 +100 -105 -105 Sell Call +17 0 -(ST-105) Buy Put -5 105-ST 0 Total 2 0 0 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus20 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 • Marcus21 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 • Marcus22 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 • Marcus23 Chapter 17 Option Valuation Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus24 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 • Marcus25 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 • Marcus26 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 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus27 Binomial Option Pricing: Text Example 100 200 50 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 • Marcus28 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 50 200 Repay loan - 50 -50 Net Payoff 0 150 53.70 150 0 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 • Marcus29 Binomial Option Pricing: Text Example 53.70 150 0 C 75 0 2C = $53.70 C = $26.85 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus30 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 Value 50 200 Call Obligation 0 -150 Net payoff 50 50 Hence 100 - 2C = 46.30 or C = 26.85 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus31 Black-Scholes Option Valuation Co = Soe -dTN(d1) - Xe -rTN(d2) d1 = [ln(So/X) + (r – d + s 2/2)T] / (s T1/2) d2 = d1 - (s T 1/2) 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. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus32 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 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus33 Call Option Example So = 100 X = 95 r = .10 T = .25 (quarter) s = .50 d = 0 d1 = [ln(100/95)+(.10-0+(.5 2/2))]/(.5 .251/2) = .43 d2 = .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 • Marcus34 Probabilities from Normal Dist. N (.43) = .6664 Table 17.2 d N(d) .42 .6628 .43 .6664 Interpolation .44 .6700 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus35 Probabilities from Normal Dist. N (.18) = .5714 Table 17.2 d N(d) .16 .5636 .18 .5714 .20 .5793 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus36 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? Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus37 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 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus38 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 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus39 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) - 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 • Marcus40 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