6. 18 POINTS A portfolio manager has a portfolio that mirrors the performance of the S&P500 so that its 3 = 1. It is worth $200 million. The S&P500 index So, is 1000. The portfolio manager would like to buy insurance against a reduction in the value of the portfolio greater than 10% in the next 3 months. The risk-free interest rate, r = 8% per year. The dividend yield on the portfolio and the S&P500 is q = 3% per year. The volatility of the index, o 20% per year. Each put contract is for 100x the index = (a) Use the Black Scholes Merton model to find the price of a European put option on the index, P. (b) Remembering that each put option contract is on 100 times the index, find the number of put option contracts to protect the portfolio against a fall of 10% in its value over the next 3 months. (c) Find the portfolio insurance costs. (d) Find the payoff from the use of put options and show the value of the insured portfolio if in 3 months, So 850. 6. 18 POINTS A portfolio manager has a portfolio that mirrors the performance of the S&P500 so that its 3 = 1. It is worth $200 million. The S&P500 index So, is 1000. The portfolio manager would like to buy insurance against a reduction in the value of the portfolio greater than 10% in the next 3 months. The risk-free interest rate, r = 8% per year. The dividend yield on the portfolio and the S&P500 is q = 3% per year. The volatility of the index, o 20% per year. Each put contract is for 100x the index = (a) Use the Black Scholes Merton model to find the price of a European put option on the index, P. (b) Remembering that each put option contract is on 100 times the index, find the number of put option contracts to protect the portfolio against a fall of 10% in its value over the next 3 months. (c) Find the portfolio insurance costs. (d) Find the payoff from the use of put options and show the value of the insured portfolio if in 3 months, So 850