Inputs
S0	45
T	2
K	50
r	2%
sigma	9%

1. Compute d1 and d2. Assume there is no dividend yield. Assume that you price the option at t=0.
2. Compute the price of the put option.
3. Suppose you want to hedge using stocks and bonds. Specify the number of shares and the face value of the bond used to hedged.

Suppose that now you want to do the delta-gamma-hedging. Specifically, to do this hedge, use another Put Option with the same strike price and underlying, but with a time to expiration of T=0.8. Call this new put option D0. With this, you construct the portfolio:

0=P0-XS0+YD0+B0

Where X is the number of shares in the hedge. Y is the number of put options D0and B0is the face value of bond.

4. What are the three conditions to find the values of X, Y and B0?
5. Find the value of X, Y and B0