Part III Consider the So -P 500 call option that has the shortest time to expiration and is closest to at-the-money. Calculate the theoretical option price based on the Black-Scholes-Merton model. Define n as the number of time periods in the Binomial model, and let a equal 1, 5, 10, 25, 50, 100, 500, and 1000. For each value of m, calculate the corresponding theoretical option price from the Binomial model. Use the Excel spreadsheet Black ScholesMerton Binomiall Oexlom to obtain the prices for both models. To obtain a call price C from the Binomial model, one needs five parameters: n, w, d, r, and p. There represent the number of periods, the binomial up factor, the binomial down factor, the risk-free rate, and the risk neutral probability, respectively. (In this scenario, however, one must also incorporate dividends.) Construct a table that shows how the values of a, d, r, p, and C change as n varies. Note that the software Black Scholes MertonBinomiall Oexlem does not report values for w, d. r, and p as a varies; it reports only