Question 3 We now wish to connect the Binomial model to the continuous time equivalent provided by Black Scholes Merton. To that end, we need to introduce a measure of volatility as measured by the standard deviation, o. To that end, consider the inputs r = 0.045, o = 0.24, T = 1/4 and So = $45 and strikes X = $40, $45, $50. For n = 1, 2, ..., 100 set 1. u = exp(o VT) and d = 1/u. 2. R = (1+r)T 3. q = (R - d)/(u -d) 4. q' = uq/R 5. a which is the smallest positive integer greater than (In(So/X) + nin(d))/ In(d/u) (10) 2 6. P[J > a] and P[J' > a] 7. Call option price Co = SoP[J' > a] - XR-"P[J > a] (11) Next, compare these to Black Scholes Merton prices