Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 26 October 2018 / Approved: 29 October 2018 / Online: 29 October 2018 (04:24:12 CET)

A peer-reviewed article of this Preprint also exists.

Sun, C.; Sheng, Q. An Exploration of a Balanced Up-Downwind Scheme for Solving Heston Volatility Model Equations on Variable Grids. Algorithms 2019, 12, 30. Sun, C.; Sheng, Q. An Exploration of a Balanced Up-Downwind Scheme for Solving Heston Volatility Model Equations on Variable Grids. Algorithms 2019, 12, 30.

Journal reference: Algorithms 2019, 12, 30
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, 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.

Subject Areas

Heston volatility model; initial-boundary value problems; finite difference approximations; up-downwind scheme; order of convergence; stability

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