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Option Pricing Models The Binomial Model The One-Period Binomial Model Suppose that we buy h shares of stocks and sell a call on this stock. The value of this portfolio is hS-C at time 0. We hope the value of this portfolio has only one outcome regardless of what the stock price does. Notice that we never specified the probabilities of the two stock price movements, they do not enter into the model. This model has a risk-neutral option pricing framework and investor’s sensitivities to risk are of no consequence. The model will accept the stock price as given and pay no attention to how risk was used to obtain the stock price. Example 87 The Two-Period Binomial Model Example 95 Pricing Put Options r=7% Early Exercise of American Put Dividends and Early Exercise The Value of European Call The Value of American Call Example Page 102 Extending the Binomial Model to n Periods * S Su Sd C Cu Cd S Su Sd Sud Suu Sdd Cuu Cud Cdd Cu Cd C 100 125 80 156.25 100 64 100 125 Dividend of 12.5 Ex-dividend price of 112.5 80 Dividend of 8 Ex-dividend price of 72 112.5(1.25)=140.625 112.5(0.8)=90 72(1.25)=90 72(0.8)=57.6 *
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