Suppose the current value of a popular stock index 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, use the Black-Scholes model to 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, explain why the implied volatility coefficient might differ from the historical volatility level.

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

(Needs to be done through excel. So please explain what formulas are used step by step so I can complete the assignment. Thank you)