Suppose the current value of a popular stock index is 653.50 and the dividend yield on the index is 2.8%. Also, the yield curve is flat at a continuously compounded rate of 5.5%.

(a) if you estimate the volatility factor for the index to be 16%, calculate the vale of an index call option with an exercise price of 670 and an expiration date in exactly three months.

(b) if the actual market price of this option is $17.40, calculate the implied volatility factor (show working)