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Stability of central finite difference schemes for the Heston PDE

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  • K. J. in 't Hout
  • K. Volders

Abstract

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments.

Suggested Citation

  • K. J. in 't Hout & K. Volders, 2010. "Stability of central finite difference schemes for the Heston PDE," Papers 1011.6532, arXiv.org.
    • Handle: RePEc:arx:papers:1011.6532
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    References listed on IDEAS

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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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