Semiclassical CEV Option Pricing Model: an Analytical Approach

TL;DR

This paper derives closed-form solutions for the semiclassical approximation of the CEV option pricing model's heat kernel, introducing novel calculations based on the Van Vleck-Morette determinant and revealing an exponential factor overlooked previously.

Contribution

It provides an analytical approach using the Van Vleck-Morette determinant for the first time in this context, enhancing the accuracy of semiclassical CEV option pricing models.

Findings

Closed-form semiclassical solutions for CEV model

Use of Van Vleck-Morette determinant in calculations

Identification of an exponential factor in the kernel

Abstract

This paper is devoted to obtain closed form solutions for the semiclassical (or WKB) approximation of the heat kernel propagator of the diffusion equation defined by the constant elasticity variance (CEV) option pricing model. One of the key points is that our calculations are based on the Van Vleck-Morette determinant instead of the Van Vleck determinant used by other authors. In fact, we compute this determinant in two different ways: by means of the solution of the classical Hamiltonian equations, and by solving the variational equations. Furthermore, the calculation reveals an exponential factor in the prefactor of the kernel not considered in previous works.