Slides_Fundamentals of Investments - Chapter 15 ppt

15 15 C h a p t e r Option ValuationOption Valuation second edition Fundamentals of Investments Valuation & Management Charles J.Corrado Bradford D.Jordan McGraw Hill / Irwin Slides by Yee-Tien (Ted) Fu © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 2 Just What is an Option Worth? © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 3 Option Valuation Our goal in this chapter is to discuss stock option prices. We will look at the fundamental relationship between call and put option prices and stock prices. Then we will discuss the Black-Scholes-Merton option pricing model. Goal © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 4 Put-Call Parity Put-call parity The difference between a call option price and a put option price for European-style options with the same strike price and expiration date is equal to the difference between the underlying stock price and the discounted strike price. © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 5 Put-Call Parity rT KeSPC − −=− C = call option price P = put option price S = current stock price K = option strike price r = risk-free interest rate T = time remaining until option expiration © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 6 Put-Call Parity  Put-call parity is based on the fundamental principle of finance stating that two securities with the same riskless payoff on the same future date must have the same price.  Suppose we create the following portfolio: c Buy 100 shares of stock X. d Write one stock X call option contract. e Buy one stock X put option contract. © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 7 Put-Call Parity © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 8 Put-Call Parity  Since the payoff for the portfolio is always equal to the strike price, it is risk-free, and therefore comparable to a U.S. T-bill.  So, cost of portfolio = discounted strike price S + P – C = Ke –rT ⇒ C – P = S – Ke –rT  If the stock pays a dividend before option expiration, then C – P = S – Ke –rT – PV(D), where PV(D) represents the present value of the dividend payment. © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 9 Work the Web  To learn more about trading options, see: http://www.ino.com http://www.optionetics.com © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 10 The Black-Scholes-Merton Option Pricing Model  Option pricing theory made a great leap forward in the early 1970s with the development of the Black-Scholes option pricing model by Fischer Black and Myron Scholes.  Recognizing the important theoretical contributions by Robert Merton, many finance professionals refer to an extended version of the model as the Black-Scholes-Merton option pricing model. [...].. .15 - 11 The Black-Scholes-Merton Option Pricing Model The Black-Scholes-Merton option pricing model states the value of a stock option as a function of six input factors: S, the current price of the underlying stock y, the dividend yield of the underlying stock K, the strike price specified in the option contract r, the risk-free interest rate over the life of the option contract... probability of the value of x McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 13 The Black-Scholes-Merton Option Pricing Model McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 14 Work the Web To learn more about the BlackScholes-Merton formula, see: http://www.jeresearch.com McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies,... reserved 15 - 15 Varying the Option Price Input Values McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 16 Varying the Underlying Stock Price McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 17 Varying the Time to Option Expiration McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 18 Varying... until the option contract expires σ, the price volatility of the underlying stock McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 12 The Black-Scholes-Merton Option Pricing Model The price of a call option on a single share of common stock, C = Se–yTN(d1) – Ke–rTN(d2) The price of a put option on a share of common stock, P = Ke–rTN(–d2) – Se–yTN(–d1) ( ) ln (S... Volatility of the Stock Price McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 19 Varying the Interest Rate McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 20 Work the Web For option trading strategies and more, see: http://www.numa.com McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 21 Measuring... Irwin ⎞ ⎟ ⎟ ⎠ X = Ke − rT © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 28 Work the Web For applications of implied volatility, see: http://www.ivolatility.com McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 29 Hedging a Portfolio with Index Options Many institutional money managers make some use of stock index options to hedge the equity portfolios... Stochastic volatility is the phenomenon of stock price volatility changing randomly over time McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 35 Implied Volatility Skews The Black-Scholes-Merton option pricing model assumes that stock price volatility is constant over the life of the option Nevertheless, the simplicity of the model makes it an excellent tool Furthermore,... Impact of Input Changes Delta measures the dollar impact of a change in the underlying stock price on the value of a stock option Call option delta = e–yTN(d1) > 0 Put option delta = –e–yTN(–d1) < 0 A $1 change in the stock price causes an option price to change by approximately delta dollars McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 22 Measuring the Impact of. .. Implied Volatility Skews McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 33 Implied Volatility Skews McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 34 Implied Volatility Skews Logically, there can be only one stock price volatility, since price volatility is a property of the underlying stock However, volatility skews do exist... percentage impact of a change in the underlying stock price on the value of a stock option Call option eta = e–yTN(d1)S/C > 1 Put option eta = –e–yTN(–d1)S/P < –1 A 1% change in the stock price causes an option price to change by approximately eta% McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 15 - 23 Measuring the Impact of Input Changes Vega measures the impact of a change . McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 7 Put-Call Parity © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 8 Put-Call. extended version of the model as the Black-Scholes-Merton option pricing model. © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 11 The Black-Scholes-Merton Option. will discuss the Black-Scholes-Merton option pricing model. Goal © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 15 - 4 Put-Call Parity Put-call parity The difference