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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/n) and d = 1/u.
2. R = (1+r/n)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)
6. P[J > a] and P[J' > a]
7. Call option price
Co = SoP[J' > a] - XR-"P[J > a]
Next, compare these to Black Scholes Merton prices.

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