27. (a) Price a ten-year down-and-in barrier call option with the following parameters: S...

27. (a) Price a ten-year down-and-in barrier call option with the following parameters: S = 100, strike K = 102, annual risk-free rate r = 2%, volatility and barrier H = 90. Use a time step of one year on the CRR tree for this problem.

(b) Price the down-and-out barrier call with the same parameters.

(c) Price the vanilla call with the same parameters.

(d) Verify that the sum of the prices you obtain in parts (a) and (b) equals the price you obtain in part (c).