Multi-Purpose Binomial Model: Fitting all Moments to the Underlying Geometric Brownian Motion
Y. S. Kim, S. Stoyanov, S. Rachev, F. Fabozzi
TL;DR
This paper introduces a generalized binomial tree model that accurately fits all moments of geometric Brownian motion, improving option pricing and unifying several classical models.
Contribution
It develops a new binomial model that matches all moments of geometric Brownian motion, extending classical models and addressing discontinuity issues in option pricing.
Findings
The model fits all moments of the underlying process.
It resolves discontinuity problems in option pricing.
The model generalizes classical binomial trees.
Abstract
We construct a binomial tree model fitting all moments to the approximated geometric Brownian motion. Our construction generalizes the classical Cox-Ross-Rubinstein, the Jarrow-Rudd, and the Tian binomial tree models. The new binomial model is used to resolve a discontinuity problem in option pricing.
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Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Probability and Risk Models