Introduction to Binomial trees Chapter 10 Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 10.1 Introduction to Binomial Trees Chapter 10
10.2 A Simple binomial model A stock price is currently $20 In three months it will be either $22 or $18 Stock Price $22 Stock price $20 Stock Price =$18 Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 10.2 A Simple Binomial Model • A stock price is currently $20 • In three months it will be either $22 or $18 Stock Price = $22 Stock Price = $18 Stock price = $20
10.3 A Call option(Figure 10.1, page 200 A 3-month call option on the stock has a strike price of 21 Stock Price= $22 Option Price $1 Stock price $20 Option price=? Stock Price=$18 Option price sO Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 10.3 Stock Price = $22 Option Price = $1 Stock Price = $18 Option Price = $0 Stock price = $20 Option Price=? A Call Option (Figure 10.1, page 200) A 3-month call option on the stock has a strike price of 21
10.4 Setting Up a riskless portfolio Consider the portfolio: long a shares short 1 call option 22△-1 18∧ Portfolio is riskless when 22A-1=18 on △=0.25 Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 10.4 • Consider the Portfolio: long D shares short 1 call option • Portfolio is riskless when 22D – 1 = 18D or D = 0.25 22D – 1 18D Setting Up a Riskless Portfolio
10.5 Valuing the portfolio (Risk-Free Rate is 12%) The riskless portfolio is long 0. 25 shares short 1 call option The value of the portfolio in 3 months is 220.25-1=4.50 The value of the portfolio today is 4.5e-0.12025=4.3670 Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 10.5 Valuing the Portfolio (Risk-Free Rate is 12%) • The riskless portfolio is: long 0.25 shares short 1 call option • The value of the portfolio in 3 months is 22´0.25 – 1 = 4.50 • The value of the portfolio today is 4.5e – 0.12´0.25 = 4.3670