4. (15 points) Show that the forward value satisfies the Black-Scholes PDE. 5. (20 points) Suppose an European call option is currently at the money, i.e. St= K. Suppose the risk-free rater O and both time to maturity T-t and volatility o are very small. Assume the underlying stock pays no dividends. Using a numerical analysis to demonstrate that the Black-Scholes European call price may be approximated by the following formula: - Ct = T-t oStV 27 Then try to prove this approximation formula according to the Black-Scholes pricing formula. 4. (15 points) Show that the forward value satisfies the Black-Scholes PDE. 5. (20 points) Suppose an European call option is currently at the money, i.e. St= K. Suppose the risk-free rater O and both time to maturity T-t and volatility o are very small. Assume the underlying stock pays no dividends. Using a numerical analysis to demonstrate that the Black-Scholes European call price may be approximated by the following formula: - Ct = T-t oStV 27 Then try to prove this approximation formula according to the Black-Scholes pricing formula