Consider a call option with strike price K > 0 in a single-period binomial model.

(i) What are the possible values of Delta (units of stock held in the replicating portfolio)?

(ii) What is the call price if K = 0?

(iii) Show that the price of a call option grows with u (upward return), the other variables being kept constant.

(b) Consider a call option with strike price K > 0 in the Black-Scholes model.

(i) What is the value of Delta if the option is in the money all the time until its expiration?

(ii) What is the value of Delta if the option is out of the money all the time until its expiration?

(iii) What is the range of possible values of Delta in any case?

(c) Under all models, show that the difference between European call value and put value with the same expiration and strike converges to the current price of the stock as the strike decreases to 0.