Need help with the calculations involved in deriving the answer for the MCQ questions below.

Options on stocks, indices and currency

1) A portfolio manager in charge of a portfolio worth $10million is concerned that the market might decline rapidly during the next six months and would like to use options on an index to provide protection against the portfolio falling below $9.5million. The index is currently standing at 500 and each contract is on 100 times the index. What should the strike price of options on the index be the portfolio has a beta of 0.5? Assume that the risk-free rate is 10% per annum and the dividend yield on both the portfolio and the index is 2% per annum.

A) 400 B) 410 C) 420 D) 430

2) For a European put option on an index, the index level is 1,000, the strike priceis1050, the time to maturity is six months, the risk-free rate is 4% per annum, and the dividend yield on the index is2 % per annum. How low can the option price be without there being an arbitrage opportunity?

A) $50.00 B) $43.11 C) $29.21 D) $39.16

3) A European at-the-money call option on a currency has four years until maturity. The exchange rate volatility is 10%, the domestic risk-free rate is 2% and the foreign risk-free rate is 5%.The current exchange rate is 1.2000. What is the value of the option?

A) 0.98N(0.25)-1.11(0.05) B) 0.98N(-0.3)-1.11N(-0.5) C) 0.98N(-0.5)-1.11N(-0.7) D) 0.98N(0.10)-1.11N(0.06)