tobinomialtrees(金融工程-華東師范大學(xué)湯銀才)-wenkub
2023-03-22 07:00:49 本頁面
【正文】 1 call option is worth ? The value of the shares is = * 20 ? The value of the option is therefore = 8 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。Introduction to Binomial Trees Chapter 9 1 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 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 Generalization (continued) : Proof with an Example ? This is known as the No Arbitrage methodology ? In our earlier example f= and D= ? If f, . f= == D S0f=*= t = 0 ST=18 ST=22 Buy call 0 1 Sell D Shares 18*= 22*= Lend at r Net Flows 0 0 ? 13 Options, Futures, and Other Derivatives, 4th edition 169。 2023 by John C. Hull Irrelevance of a Stock’s E(R) (continued) ? The probability of an increase in the stock price is irrelevant because options are redundant securities ? In our twostep models, we form a riskless portfolio with stock and the option ? Thus, the return/payoff from the option is offset by the return on the stock and the portfolio return is the same in both states ? Thus, no matter what the probability of a stock increase, the answer is the same ? 17 Options, Futures, and Other Derivatives, 4th edition 169。 2023 by John C. Hull RiskNeutral Valuation (Continued) ? ? = [ p ?u + (1 – p )?d ]erT ? The variables p and (1 – p ) can be interpreted as the riskneutral probabilities of up and down movements ? The value of a derivative is its expected payoff in a riskneutral world discounted at the riskfree rate ? Figure bees S0u
教學(xué)課件相關(guān)推薦
鄂ICP備17016276號(hào)-1