Consider an eight-month call option on the S&P 100 index with strike price 1150. The current S&P index is 1054.50, and its dividend yield is 2%. The interest is 1% per annum. The volatility of the index is 20% per annum. (In your solution, report index and option values with two digits after decimal points but report u, d, and q with four decimal numbers.)

(a) Show an eight-step binomial model for the S&P 100 index on a spreadsheet. Display the result of your binomial model.

(b) On each node of your binomial model, what is the risk-neutral probability for the index to go down in the next step?

(c) Suppose you have five contracts of S&P 100 index options, what is the value of your contracts (round to a dollar)?

(d) Is it optimal to exercised these call option contracts early on some nodes of the price tree? Does your answer conflict with the rule of no early exercise of American call options?

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Answer a Below is an example of an eightstep binomial model for the SP 100 index on a spreadsheet St... View the full answer