Consider a one-period binomial tree. The length of the period is h years. The stock price moves from S to S × u or to S × d, 0 < d < u.

The stock pays no dividends. Let α be the continuously compounded expected rate of return on the stock. Consider a one-period put option on the stock with strike price S × k, for some k > 0. 

Let γ(k) denote the continuously compounded expected rate of return on the put option, considered as a function of k. 

Determine γ(k). Your answer should involve k, r, α, h, u and d. Note that k ranges from 0 to ∞.