Let S be the price of a stock at time t with t = 0 being today. Assume $80. The volatility of the stock is 30% per annum. The expected return of the stock is 12%. The risk-free rate is 10%. So = Let f(S) = 0 if S 70, (S) = S 70 if 70 S 75 and (S) = 5 if S > 75. (a) Graph y = f(S). Construct the derivative whose payoff is given by this graph. (b) Use Black-Scholes to price this derivative (c) Assuming Black-Scholes, compute the delta of this derivative. Let S be the price of a stock at time t with t = 0 being today. Assume $80. The volatility of the stock is 30% per annum. The expected return of the stock is 12%. The risk-free rate is 10%. So = Let f(S) = 0 if S 70, (S) = S 70 if 70 S 75 and (S) = 5 if S > 75. (a) Graph y = f(S). Construct the derivative whose payoff is given by this graph. (b) Use Black-Scholes to price this derivative (c) Assuming Black-Scholes, compute the delta of this derivative