Semiclassical CEV Option Pricing Model: an Analytical Approach

2024/11/27 by José A. Capitán, Capitán, Jose A., Jose Lope-Alba +3
Economics, Econometrics and Finance · Energy · Engineering · #Climate Change Policy and Economics #Electric Vehicles and Infrastructure #Energy, Environment, and Transportation Policies #FOS: Economics and business #Mathematical Finance (q-fin.MF)

paper · pdf · doi:10.48550/arxiv.2411.18154

openalex publication_date 2024/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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