A put option on the S&P 500 has an exercise price of 500 and a time to maturity of one year. The risk free rate is 7% and the dividend yield on the index is 3%. The volatility of the index is 2% per annurn and the current level of the index is 500. A nancial institution has a short position in the option. a) Calculate the delta, garrnna, and vega of the position. Explain how they can be interpreted. b) How can the position he made delta neutral? c) Suppose that one week later the index has increased to 515. Hotsr can delta neutrality be preserved