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A Fitted Finite Volume Method for the Valuation of Options on Assets with Stochastic Volatilities

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Abstract

In this paper, we present a finite volume method for a two-dimensional Black-Scholes equation with stochastic volatility governing European option pricing. In this work, we first formulate the Black-Scholes equation with a tensor (or matrix) diffusion coefficient into a conservative form. We then present a finite volume method for the resulting equation, based on a fitting technique proposed for a one-dimensional Black-Scholes equation. We show that the method is monotone by proving that the system matrix of the discretized equation is an M-matrix. Numerical experiments, performed to demonstrate the usefulness of the method, will be presented.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Sun Yat-sen University, 811, Kaohsiung, Taiwan

    C.-S. Huang & C.-H. Hung

  2. School of Mathematics and Statistics, The University of Western Australia, Crawley, 6009, Australia

    S. Wang

Authors
  1. C.-S. Huang
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  2. C.-H. Hung
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  3. S. Wang
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Correspondence to C.-S. Huang.

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Huang, CS., Hung, CH. & Wang, S. A Fitted Finite Volume Method for the Valuation of Options on Assets with Stochastic Volatilities. Computing 77, 297–320 (2006). https://doi.org/10.1007/s00607-006-0164-4

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  • DOI: https://doi.org/10.1007/s00607-006-0164-4

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