Exercise 9.3.1 The price volatility of the binomial model should match that of the actual stock in the limit. As q does not play a direct role in the BOPM, there is more than one way to assign u and

d. Suppose we require that q = 0.5 instead of ud = 1.

(1) Show that u = exp



μτ

n

+σ

*

τ

n



, d = exp



μτ

n

−σ

*

τ

n



satisfy requirements (9.13) and (9.14) as equalities. (2) Is it valid to use the probability 0.5 during backward induction under these new assignments?