Part III a) Consider the SexP 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 n equal 1, 5, 10, 25, 50, 100, 500, and 1000. For each value of n, calculate the corresponding theoretical option price from the Binomial model. Use the Excel spreadsheet Black Scholes Merton Binomiall Oe.xism to obtain the prices for both models. b) To obtain a call price C from the Binomial model, one needs five parameters: n, u, d, r, and p. These 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 Merton Binomiall Oe. xism does not report values for u, d, r, and p as a varies; it reports only 'In calculating volatilities use the following conventions: For daily calculations use all 124 daily index observations over six months. This yields 123 daily returns. Use the first 60 returns to estimate volatility for the first three months. Use the last 63 returns to estimate volatility for the last three months. For weekly calculations begin with the first Friday in the data, January 5, 2007, and go to the last Friday in the data, June 29, 2007. This yields 25 weekly returns. The first 12 returns correspond to the first three months, and the last 13 returns correspond to the last three months. Because there is no observation on Friday, April 6, replace it with the preceding day's observation. " The stock index return data in Table 3 of SecondCityOptionsCase_Data10e.xlex are from the Center for Research in Security Prices (CRSP). The interest rate data are from Federal Reserve Economic Data (FRED) at www.research.stlouisfed.org. The daily dividend estimates calculated in Table 3 are not actual forecasts of daily dividends that could be made on July 2, 2007, which are what one should use as inputs for the option pricing models. One reason is that the SPX dividend estimates in Table 3 consist of realized, not estimated, dividends for the dates in question. They are calculated using SPX returns from CRSP. Another reason is that when estimating the OEX dividends in Table 3, the percentage of total return due to dividends for SPX proxies for the analogous percentage of total return due to dividends for OEX The rationale is that SPX returns, unlike OEX returns. are directly available from CRSP To obtain accurate