9.1 Introduction to Binomial trees Chapter g Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 9.1 Introduction to Binomial Trees Chapter 9
9.2 A Simple binomial model of stock Price movements In a binomial model the stock price at the BEGINNING of a period can lead to only 2 stock prices at the ENd of that period Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 9.2 A Simple Binomial Model of Stock Price Movements • In a binomial model, the stock price at the BEGINNING of a period can lead to only 2 stock prices at the END of that period
93 Option pricing Based on the assumption of No arbitrage opportunities Procedures i Establish a portfolio of stock and option → Value the portfolio no arbitrage opportunities no uncertainty at maturity no risk with the portfolio risk-free interest earned i Value the option Risk-free interest =value of portfolio today Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 9.3 Option Pricing Based on the Assumption of No Arbitrage Opportunities • Procedures: ➔ Establish a portfolio of stock and option ➔ Value the Portfolio ➢ no arbitrage opportunities ➢ no uncertainty at maturity ➢ no risk with the portfolio ➢ risk-free interest earned ➔ Value the option ➢ Risk-free interest = value of portfolio today
94 A Simple binomial model: Example 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, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 9.4 A Simple Binomial Model: Example • 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
9.5 A Call option a3-month call option on the stock has a strike price of $21 Figure 9.1(P202) Stock Price $22 Option price= $1 Stock price= $20 Option Price=? Stock Price =$18 Option price $0 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 9.5 Stock Price = $22 Option Price = $1 Stock Price = $18 Option Price = $0 Stock price = $20 Option Price=? A Call Option • A 3-month call option on the stock has a strike price of $21. • Figure 9.1 (P.202)