The S&P500 index is currently at 1300. Volatility is 10%, and interest rates are 2.5%. Price a 3 month European put option with strike price 1400. The firms in the index pay dividends at a continuous rate of 1.5%. Suppose you had written the S&P500 Index option from the previous question. You now need to hedge the option, and in order to do so, have decided to calculate Delta (), Gamma () and Vega (V ).

Calculate the three quantities using the finite difference technique, using of 0.001. Hint: This may be done quite quickly in excel.