A fund manager has a well-diversified portfolio that is worth $100 million. The value of the S&P 500 is 2,200 and the portfolio manager would like to buy insurance against a reduction of more than 5% in the value of the portfolio over the next 3 months. The risk-free interest rate is 6% per annum. The dividend yield on both the portfolio and the S&P 500 is 1%. The volatility of the index is 18% per annum. One index option contract is on 300 times the index (i.e. contract size = 300).

i) What is the strike price of the option written on the S&P 500 that protects against a 5% drop in the value of the portfolio over the next 3 months?

ii) What is the number of contracts (rounded to the closest integer) needed?