A stock index is currently at 858. A call option with a strike of 850 and 17 days (= 0.047 years) to maturity costs 23.50. 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 28%, what would happen to the call’s value? 

(c) If all the other parameters remained the same, what would the option value be after one week (i.e., with 10 days or 0.027 years left to maturity)?