Assume the Black-Scholes framework. A non-dividend-paying stock S with price process (SL) is currently priced at So = 50 and its annual volatility is 40%. The continuously compounded annual riskless rate is 2%. Consider a call-on-call" derivative D with the maturity of T = 1.5 such that the derivative holder has a right to buy a unit of an European call C at T = 1.5 for a price K. The call C is written on S and is at-the-money at T (i.e. the strike of C is exactly Sr) and expires at (T+T') where T' = 0.5. The price K is pre-determined at time 0 using the time-0 price of a 50-strike (T+T')-year call written on S. (a) Calculate the value of K (b) Determine the time-T price of the call C in terms of St. (c) Calculate the time-0 price of the derivative D. Assume the Black-Scholes framework. A non-dividend-paying stock S with price process (SL) is currently priced at So = 50 and its annual volatility is 40%. The continuously compounded annual riskless rate is 2%. Consider a call-on-call" derivative D with the maturity of T = 1.5 such that the derivative holder has a right to buy a unit of an European call C at T = 1.5 for a price K. The call C is written on S and is at-the-money at T (i.e. the strike of C is exactly Sr) and expires at (T+T') where T' = 0.5. The price K is pre-determined at time 0 using the time-0 price of a 50-strike (T+T')-year call written on S. (a) Calculate the value of K (b) Determine the time-T price of the call C in terms of St. (c) Calculate the time-0 price of the derivative D