Consider 0.5 as the volatility of the stock and use the rate r = 0.0125 as annual risk-free rate. Assume you want to build a portfolio of options containing one call option with strike K1 = 420, and one put option with strike K2 = 460. Let C1(t, x) denotes the call option pricing function. Let P2(t, x) denotes the put option pricing function. Let the maturity T = 12 months. Using the adjusted closing price of 437.5 as the initial stock price.

1. Compute the option prices C1, P2 on that date.

2. Compute the Delta () of this portfolio

3. Compute the Gamma () of this portfolio .