Suppose the current value of the Standard and Poor’s 500 indexes is XXXXXXXXXXand the dividend yield on the index is 2.8 percent. Also, the yield curve is flat at a continuously compounded rate of 5.5...

Suppose the current value of the Standard and Poor’s 500 indexes is 653.50 and the dividend yield on the index is 2.8 percent. Also, the yield curve is flat at a continuously compounded rate of 5.5 percent.

a. If you estimate the volatility factor for the index to be 16 percent, calculate the value 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 its implied volatility coefficient.

c. Besides volatility estimation error, explain why your valuation and the option’s traded price might differ from one another.