Edgeworth Binomial Trees

Mark Rubinstein.

No RPF-275, Research Program in Finance Working Papers from University of California at Berkeley

Abstract: This paper develops a simple technique for valuing European and American derivatives with underlying asset risk-neutral returns which depart from lognormal in terms of prespecified non-zero skewness and greater-than-three kurtosis. Instead of specifying the entire risk-neutral distribution by the riskless return and volatility (as in the Black-Scholes case), this distribution is specified by its third and fourth central moments as well. An Edgeworth expansion is used to transform a standard binomial density into a unimodal standardized discrete density -- evaluated at equally-spaced points -- with approximately the prespecified skewness and kurtosis. This density is in turn adjusted to have a mean equal to the riskless return (adjusted for the payout return, if any) and to a prespecified volatility. European derivatives are then easily valued by using this risk-neutral density to weight their possible payoffs.

Date: 1997-11-01
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