This is a financial mathematic question.

A cash-or-nothing binary call option is a derivative contract with the payoff function a Ac(S) = { 1 if S >K, 0 if S K. 2 (a) (30 points) Derive the (Black-Scholes) exact pricing formulas for both the binary call C(0, So) and the put P(0, So) as a function of the initial price So and the expiry time T, the interest rate r, and the volatility o. (Hint. Use the equation C(0, So) = e-rT(Ac(ST)) to find the price of the binary call option. You can use a similar method for the binary put option.) (b) (10 points) Give the relationship between the binary put and call price where both options have the same strike K and maturity T. (Hint. Try to find an equation similar to the put-call parity for European options.) (c) (20 points) Derive the exact formula for the Greek delta of the binary put and call. A cash-or-nothing binary call option is a derivative contract with the payoff function a Ac(S) = { 1 if S >K, 0 if S K. 2 (a) (30 points) Derive the (Black-Scholes) exact pricing formulas for both the binary call C(0, So) and the put P(0, So) as a function of the initial price So and the expiry time T, the interest rate r, and the volatility o. (Hint. Use the equation C(0, So) = e-rT(Ac(ST)) to find the price of the binary call option. You can use a similar method for the binary put option.) (b) (10 points) Give the relationship between the binary put and call price where both options have the same strike K and maturity T. (Hint. Try to find an equation similar to the put-call parity for European options.) (c) (20 points) Derive the exact formula for the Greek delta of the binary put and call