please answer 2 a,b,c,d as they all correlate to the same question. I will leave excellent review

2. Suppose that the price S(t) of a share follows the GBM with parameters S, H, O, T. Consider an option with the expiration time T and a payoff function Kif S(T) K. (Note that if a portfolio consists of 1 share and 1 such option then the payoff of at least K is guaranteed.) (a) Compute the no-arbitrage price of this option. (b) Suppose now that the above share provides a dividend yield of rate a which is paid continuously and is reinvested in the share. What is the price of the derivative with the same payoff function? 1 (c) Suppose that a discrete proportionate dividend of rate d is paid at time T/2 and is immediately reinvested in the share. The expiration time of the option is t, 0 K. (Note that if a portfolio consists of 1 share and 1 such option then the payoff of at least K is guaranteed.) (a) Compute the no-arbitrage price of this option. (b) Suppose now that the above share provides a dividend yield of rate a which is paid continuously and is reinvested in the share. What is the price of the derivative with the same payoff function? 1 (c) Suppose that a discrete proportionate dividend of rate d is paid at time T/2 and is immediately reinvested in the share. The expiration time of the option is t, 0