Show that the Black-Scholes formula for the price of a call option, C(S, t), satisfies the

following condition:

(a) Show that the Black-Scholes formula for the price of a call option, C(S,t), satisfies the following condition: C(S,t) > [S --(T-1) K]*. In order to answer this question, use the Black-Scholes formula. Do not use put-call parity, or a general argument (not specific to the Black-Scholes setting) that establishes no-arbitrage bounds for option prices. (b) Under Black-Scholes assumptions, the price of an asset-or-nothing digital call option with strike price K and maturity date T is given by CA(S,t) = S(di), where 0 (s) is the standard normal cdf, and log(S/K) + (r + 02/2)(T t) di OVT-t Calculate the delta of this option, 54. What is the limit of at-the-money 8A as t +T? (a) Show that the Black-Scholes formula for the price of a call option, C(S,t), satisfies the following condition: C(S,t) > [S --(T-1) K]*. In order to answer this question, use the Black-Scholes formula. Do not use put-call parity, or a general argument (not specific to the Black-Scholes setting) that establishes no-arbitrage bounds for option prices. (b) Under Black-Scholes assumptions, the price of an asset-or-nothing digital call option with strike price K and maturity date T is given by CA(S,t) = S(di), where 0 (s) is the standard normal cdf, and log(S/K) + (r + 02/2)(T t) di OVT-t Calculate the delta of this option, 54. What is the limit of at-the-money 8A as t +T