Recombining binomial tree for constant elasticity of variance process

TL;DR

This paper introduces a recombining binomial tree method tailored for pricing American put options when the underlying follows a CEV process, ensuring convergence and computational efficiency.

Contribution

It develops a novel recombining binomial tree based on finite difference schemes to model the CEV process with linear complexity.

Findings

The method accurately prices American put options under CEV.

Numerical experiments confirm convergence and high accuracy.

The approach is computationally efficient for practical use.

Abstract

The theme in this paper is the recombining binomial tree to price American put option when the underlying stock follows constant elasticity of variance(CEV) process. Recombining nodes of binomial tree are decided from finite difference scheme to emulate CEV process and the tree has a linear complexity. Also it is derived from the differential equation the asymptotic envelope of the boundary of tree. Conducting numerical experiments, we confirm the convergence and accuracy of the pricing by our recombining binomial tree method. As a result, we can compute the price of American put option under CEV model, effectively.