The payoff at maturity T of an cashornothing call option with strike K is 1 if S(T) K, and 0 otherwise. Similarly, the payoff at maturity T of an cashornothing put option with strike K is 1 if S(T) K, and 0 otherwise.

(i) (1 point) What is the put-call parity relationship for cashornothing options?

(ii) (4 points) Use risk-neutral pricing to find the Black-Scholes values of cashor nothing options.

(iii) (4 points) Find the limit of the Black-Scholes values of cashornothing options as volatility goes to 0 and to infinity.

(iv) (4 points) Find the Black-Scholes formula for the Delta and Gamma of cashor nothing options.