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

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Department of Mathematics and Center for Astrophysics, Space Physics, and Engineering Research, Baylor University, One Bear Place, Waco, TX 76798-7328, USA
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Algorithms 2019, 12(2), 30; https://doi.org/10.3390/a12020030
Received: 26 October 2018 / Revised: 4 January 2019 / Accepted: 6 January 2019 / Published: 22 January 2019
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. View Full-Text
Keywords: Heston volatility model; initial-boundary value problems; finite difference approximations; up-downwind scheme; order of convergence; stability Heston volatility model; initial-boundary value problems; finite difference approximations; up-downwind scheme; order of convergence; stability
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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.

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