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Risk Neutral Pricing and Financial Mathematics: A Primer by John L. Teall, Peter M. Knopf

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image (5.20)

or:

c0=S0[j=aTT!j!(Tj)!qj(1q)TjujdTj(1+r)T]X(1+r)T[j=aTT!j!(Tj)!qj(1q)Tj]

image

or, in shorthand form:12

c0=S0B[T,q]X(1+r)TB[T,q]

image

where q′=qu/(1+r) and 1−q′=d(1−q)/(1+r). The values q′, q, and T are the parameters for the two binomial distributions. Three points are worth further discussion regarding this simplified binomial model:

1. First, as T approaches infinity, the binomial distribution will approach the normal distribution, ...

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