In the binomial model, suppose now that the stock pays dividends proportional to the stock price at the end of each period. That is, the ex-dividend price is given by (1 − δ)S, when the cum-dividend price is S, for some δ, 0 < δ < 1. Construct the binomial lattice for the stock price process, and calculate the premiums of the call and put options in the setting of Exercise 8.5 with δ = 0.1. Is the binomial lattice recombining? Also, does the put–call parity hold even in this case? Hint: The risk-neutral probability is determined through (6.24).