The S&P 500 index is currently at 1101. A call option with a strike of 1075 and 17 trading days (= 0.067 years) to maturity costs 36.20. Assume an interest rate of 3%. For simplicity, assume also that the dividend yield on the index is zero.

(a) What is the implied volatility? 

(b) If implied volatility went up to 20%, what would happen to the call’s value? 

(c) If the other parameters remained the same, what would the option value be after one week (i.e., with 12 trading days or 0.0476 years left to maturity)? 

(d) Finally, how would your answer to part (a) change if the dividend yield were taken to be 2% instead of zero?