Mathematical Finance Question:

Verify the results in Example 10.7. (use r=0.1 (not 0.01), =0.15, K=80, and N=4; also, "t" should be "t".)

That is, prove the American call price using a binomial tree with known dollar dividends.

Erample 10.7. We price an American call option on such a dividend-paying stock. Suppose there are inputs S(0,0) = 100, DI = 0, D2 = 1, D3 = 0 and D4 = 0 Thus, with 1, R-exp(0.01), u = exp(oVit) = exp(0.15), d = 1/u. D2 R2 D2 Do 0.81873075 D, 0.90483742 D30 The American call price is $45.67. In this case notice that the European and American call prices are the same, and there is no early exercise. With 134 10 Dividends an American put option, there are always situations where it is optimal to exercise early; with the American call, as here, there may not be optimal choices to exercise early Erample 10.7. We price an American call option on such a dividend-paying stock. Suppose there are inputs S(0,0) = 100, DI = 0, D2 = 1, D3 = 0 and D4 = 0 Thus, with 1, R-exp(0.01), u = exp(oVit) = exp(0.15), d = 1/u. D2 R2 D2 Do 0.81873075 D, 0.90483742 D30 The American call price is $45.67. In this case notice that the European and American call prices are the same, and there is no early exercise. With 134 10 Dividends an American put option, there are always situations where it is optimal to exercise early; with the American call, as here, there may not be optimal choices to exercise early