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Unformatted text preview: tree. 140 Multiple Periods in the Binomial Option Pricing Model ✟ ✟✟ ✟✟ ❍ ❍❍ ❍ ✟ ✟✟ ✏ ✏✏ ✏✏ ✏ ✏✏ ￿￿ ￿￿ ￿￿ ￿ ￿ ❍❍ ❍ ❍ ✏ ✏✏ ✏✏ ✏ ✏✏ ￿￿ ￿￿ ￿￿ ￿ ￿ Note that we lost the “linkup” between nodes after the dividend.1 We want to price a call option with an exercise price . The state price probabilities are the same as the ones we calculated above, If the option was European we could do nothing next month, we get the following picture of option prices: ✟ ✟✟ ✟✟ ❍ ❍❍ ❍ ✟ ✟✟ ✏ ✏ ✏✏ ✏✏ ✏✏ ￿￿ ￿￿ ￿￿ ￿ ￿ ❍❍ ❍ ❍ ✏ ✏✏ ✏✏ ✏ ✏ ￿￿ ￿￿ ￿￿ ￿ ￿ But what if the option is American? Then, next period, just before the ex dividend date, we can exercise the option, receiving . In the case above, if the stock price goes up to 110 at time 1, we could exercise the option, earning . This is better than the value of letting the option “stay alive,” which is calculated in the tree above to be 7.14. 1 If the dividend had been proportional to the price, that would not have happened. Can you see why? 15.5 Implementing the binomial option formula. ✟ ✟✟ ✟✟ ❍ ❍❍ 141 ✯ ✟ ✟✟ ❍ ❍❍ ❍ ❥ ❍ The American feature of the call option has value, compare the price of an European call, equal to 5.87, to the price of an American call, 7.875. 15.5 Implementing...
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