PROBLEM 8. [10 points) A cash-or-nothing call option is a European type call option that pays cash of the amount B if S > E at expiration, otherwise it pays nothing. (a) What is the payoff function of the cash-or-nothing call option? (b) Explain in one paragraph why the Black-Scholes analysis can be applied to the cash- or-nothing call option. (c) What is partial differential equation that the value function of a cash-or-nothing call, V(S,t) satisfies? (d) What are the boundary conditions and final condition? (e) Derive a formula for V(S,t). PROBLEM 8. [10 points) A cash-or-nothing call option is a European type call option that pays cash of the amount B if S > E at expiration, otherwise it pays nothing. (a) What is the payoff function of the cash-or-nothing call option? (b) Explain in one paragraph why the Black-Scholes analysis can be applied to the cash- or-nothing call option. (c) What is partial differential equation that the value function of a cash-or-nothing call, V(S,t) satisfies? (d) What are the boundary conditions and final condition? (e) Derive a formula for V(S,t)