Numerical Method for Highly Non-linear Mean-reverting Asset Price Model with CEV-type Process

TL;DR

This paper introduces a novel mean-reverting asset price model with a highly non-linear CEV-type volatility process, and develops a truncated EM numerical method to analyze it for pricing path-dependent financial products.

Contribution

It proposes a new stochastic model with non-linear volatility and creates a truncated EM scheme for its numerical analysis, addressing the lack of closed-form solutions.

Findings

The truncated EM method effectively approximates the model's solutions.

The approach enables valuation of complex path-dependent financial derivatives.

The model captures stochastic volatility with non-linear dynamics.

Abstract

It is well documented from various empirical studies that the volatility process of an asset price dynamics is stochastic. This phenomenon called for a new approach to describing the random evolution of volatility through time with stochastic models. In this paper, we propose a mean-reverting theta-rho model for asset price dynamics where the volatility diffusion factor of this model follows a highly non-linear CEV-type process. Since this model lacks a closed-form formula, we construct a new truncated EM method to study it numerically under the Khasminskii-type condition. We justify that the truncated EM solutions can be used to evaluate a path-dependent financial product.