You currently hold a European put option with following parameters: S=$56, X=$52, T=1.25 years, and =0.33. There are two other options written on the same stock: the first being a European put with X1 = $57 and T1 = 0.75 years, and the second being a European call with X2 = $54 and T2 = 1.3 years. The risk-free interest rate is 5.2%.

A) Calculate the price, delta and gamma for each option.

B) Find the combination of your original option and the first option so that you invest the same dollar amount as before, but the portfolio is delta-neutral. Calculate the change of your investment and change in delta with and without the hedge if the stock price moves to S=$53 after 0.005 years.

C) Repeat B) with the second option.

D) Find the combination of all three options so that you invest the same dollar amount as before, but the portfolio is both delta-neutral and gamma-neutral. Calculate the change of your investment and change in delta with and without the hedge if the stock price moves to S=$53 after 0.005 years.

E) Find the combination of your original option and the first option so that you invest the same dollar amount as before, but the portfolio is gamma-neutral. Calculate the change of your investment and change in delta with and without the hedge if the stock price moves to S=$53 after 0.005 years.

(Note: It is highly advisable to perform all initial calculations in Excel and then refer to cells for derived quantities. This is especially important when solving the simultaneous equations in order to minimize rounding off errors.)