APPENDIX C

Expanding the von Neumann Stability Mode for the Discretized Black-Scholes Equation

From section 9.3.2 Gaussian Kurtosis (and Skew = 0), Faster Convergence, the von Neumann stability mode Ci,j = ζimageseikx is

images

Then using only the up and down probabilities,

images

images

Next, expanding in powers of Δx,

images

which, in turn, leads to

images

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