Hermite Binomial Trees: A Novel Technique for Derivatives Pricing

Edgeworth binomial trees were applied to price contingent claims when the underlying

return distribution is skewed and leptokurtic, but with the limitation of working only

for a limited set of skewness and kurtosis values. Recently, Johnson binomial trees

were introduced to accommodate any skewness-kurtosis pair, but with the drawback of

numerical convergence issues in some cases. Both techniques may suffer from non-exact

matching of the moments of distribution of returns. A solution to this limitation is

proposed here based on a new technique employing Hermite polynomials to match exactly

the required moments. Several numerical examples illustrate the superior performance of

the Hermite polynomials technique to price European and American options in the context

of jump-diffusion and stochastic volatility frameworks and options with underlying

asset given by the sum of two lognormally distributed random variables.