1096 The Journal of finance The example can be extended to a multiperiod framework in which the price of the underlying stock can take on only one of two values at any time t given the price of the stock at t-1. Consider the case in which a non-dividend paying stock's holding period return is 1. 175 in all up states and. 85 in all down states Given an initial stock price of $100, these return parameters imply the four-period price pattern shown in Figure 1 Assume that we wish to value a call option which matures at the end of peric and has an exercise price of $100. Given a riskless interest rate of 1.25%per period(5% per year, assuming a one-year maturity), the sequence of option valt corresponding to the stock prices in Figure 1 is given in Figure 2. In Figure 2 the prices $90.61 and $37. 89 are the values of the call obtainable by exercising at maturity. For those states at maturity where the price of the stock falls below the exercise price of $100, the option expires worthless. Each of the time 3 option prices is obtained from (4). Similarly, the prices at time 2, 1, and 0 are obtained by recursive application of (4)resulting in a current call option price f1441 99.88 99.75 100.00 85.00 99.75 72.16 61.41 Figure 1. Price Path of Underlying Stock