An Exploration of a Balanced Up-Downwind Scheme for Solving Heston Volatility Model Equations on Variable Grids

Chong Sun,Qin Sheng

doi:10.3390/a12020030

Abstract

This paper studies an effective finite difference scheme for solving two-dimensional Heston stochastic volatility option-pricing model problems. A dynamically balanced up-downwind strategy for approximating the cross-derivative is implemented and analyzed. Semi-discretized and spatially nonuniform platforms are utilized. The numerical method comprised is simple and straightforward, with reliable first order overall approximations. The spectral norm is used throughout the investigation, and numerical stability is proven. Simulation experiments are given to illustrate our results.

Highlights

Demand for highly effective, efficient, and reliable numerical methods has grown increasingly high for solving option-trading modeling equations involving cross-derivative terms
In this investigation, targeted at European options that can only be exercised on dates of maturity, we propose and analyze a new and dynamically balanced up-downwind finite difference method in the pursuit
Classic BSM models often cannot fit ideally into the market data observed nowadays [4]. This may be due to the fact that, in modern financial markets, are stock prices subject to risk, and the estimate of riskiness is typically subject to significant uncertainty

Summary

Introduction

Demand for highly effective, efficient, and reliable numerical methods has grown increasingly high for solving option-trading modeling equations involving cross-derivative terms. Desirable computational procedures are, in general, difficult to obtain, due to challenges from the participation of cross-derivatives [1,2]. Classic BSM models often cannot fit ideally into the market data observed nowadays [4]. This may be due to the fact that, in modern financial markets, are stock prices subject to risk, and the estimate of riskiness is typically subject to significant uncertainty. To incorporate an additional source of randomness into an option pricing model, Heston proposed a more refined approach, based on the concept of stochastic volatility [5,6,7]

Methods

Results

Conclusion