tobinomialtrees(金融工程-華東師范大學湯銀才)-展示頁
2025-03-09 07:00本頁面
【正文】 the portfolio value today is S0 D – f ? Hence, ? = S0 D – (S0u D – ?u )e–rT 11 Options, Futures, and Other Derivatives, 4th edition 169。 2023 by John C. Hull Generalization ? Consider a derivative that lasts for time T and that is dependent on a stock ? Figure () S0u ?u S0d ?d S0 ? 9 Options, Futures, and Other Derivatives, 4th edition 169。 2023 by John C. Hull Valuing the Portfolio ( with RiskFree Rate 12% ) ? The riskless portfolio is: LONG shares SHORT 1 call option ? The value of the portfolio in 3 months is 22 * 1 = = 18 * ? The value of the portfolio today is *= 7 Options, Futures, and Other Derivatives, 4th edition 169。 2023 by John C. Hull Stock Price = $22 Option Price = $1 Stock Price = $18 Option Price = $0 Stock price = $20 Option Price=? A Call Option ? A 3month call option on the stock has a strike price of $21. ? Figure () 5 Options, Futures, and Other Derivatives, 4th edition 169。 2023 by John C. Hull 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 ? riskfree interest earned ? Value the option ? Riskfree interest = value of portfolio today 3 Options, Futures, and Other Derivatives, 4th edition 169。Introduction to Binomial Trees Chapter 9 1 Options, Futures, and Other Derivatives, 4th edition 169。 2023 by John C. Hull 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 2 Options, Futures, and Other Derivatives, 4th edition 169。 2023 by John C. Hull 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 4 Options, Futures, and Other Derivatives, 4th edition 169。 2023 by John C. Hull ? Consider the Portfolio: LONG D shares SHORT 1 call option ? Figure bees ? Portfolio is riskless when 22D – 1 = 18D or D = 22D – 1 18D Setting Up a Riskless Portfolio S0 = 20 6 Options, Futures, and Other Derivatives, 4th edition 169。 2023 by John C. Hull Valuing the Option
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