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Weak approximation of Heston model by discrete random variables

Author

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  • Lenkšas, A.
  • Mackevičius, V.

Abstract

We construct a first-order weak split-step approximation for the solution of the Heston model that uses, at each step, generation of two discrete two-valued random variables. The Heston equation system is split into the deterministic part, solvable explicitly, and the stochastic part that is approximated by discrete random variables. The approximation is illustrated by several simulation examples, including applications to option pricing.

Suggested Citation

  • Lenkšas, A. & Mackevičius, V., 2015. "Weak approximation of Heston model by discrete random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 113(C), pages 1-15.
    • Handle: RePEc:eee:matcom:v:113:y:2015:i:c:p:1-15
    DOI: 10.1016/j.matcom.2015.02.003
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    References listed on IDEAS

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    1. Syoiti Ninomiya & Nicolas Victoir, 2008. "Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 107-121.
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    5. 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.
    6. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
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