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 (Γ) of this portfolio.