Computing the CEV option pricing formula using the semiclassical approximation of path integral

TL;DR

This paper introduces a novel numerical method based on semiclassical path integral approximation for efficiently and accurately computing CEV option prices, outperforming traditional methods especially in challenging parameter regimes.

Contribution

The paper develops a new semiclassical path integral approach for CEV option pricing, reducing computational time while maintaining accuracy.

Findings

The method is efficient and accurate for European call options.

It outperforms the standard non-central chi-square approach in speed.

The approach is particularly effective for small maturities and low volatility.

Abstract

The Constant Elasticity of Variance (CEV) model significantly outperforms the Black-Scholes (BS) model in forecasting both prices and options. Furthermore, the CEV model has a marked advantage in capturing basic empirical regularities such as: heteroscedasticity, the leverage effect, and the volatility smile. In fact, the performance of the CEV model is comparable to most stochastic volatility models, but it is considerable easier to implement and calibrate. Nevertheless, the standard CEV model solution, using the non-central chi-square approach, still presents high computational times, specially when: i) the maturity is small, ii) the volatility is low, or iii) the elasticity of the variance tends to zero. In this paper, a new numerical method for computing the CEV model is developed. This new approach is based on the semiclassical approximation of Feynman's path integral. Our simulations show that the method is efficient and accurate compared to the standard CEV solution considering the pricing of European call options.