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The Heston Stochastic-Local Volatility Model: Efficient Monte Carlo Simulation

Author

Listed:
  • ANTHONIE W. VAN DER STOEP

    () (Derivatives Research and Validation Group, Rabobank, Graadt van Roggenweg 400, 3531 AH, Utrecht, The Netherlands;
    CWI — National Research Institute for Mathematics and Computer Science, Science Park 123, 1098 XG, Amsterdam, The Netherlands)

  • LECH A. GRZELAK

    (Derivatives Research and Validation Group, Rabobank, Graadt van Roggenweg 400, 3531 AH, Utrecht, The Netherlands;
    CWI — National Research Institute for Mathematics and Computer Science, Science Park 123, 1098 XG, Amsterdam, The Netherlands)

  • CORNELIS W. OOSTERLEE

    (Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands;
    CWI — National Research Institute for Mathematics and Computer Science, Science Park 123, 1098 XG, Amsterdam, The Netherlands)

Abstract

In this paper we propose an efficient Monte Carlo scheme for simulating the stochastic volatility model of Heston (1993) enhanced by a nonparametric local volatility component. This hybrid model combines the main advantages of the Heston model and the local volatility model introduced by Dupire (1994) and Derman & Kani (1998). In particular, the additional local volatility component acts as a "compensator" that bridges the mismatch between the nonperfectly calibrated Heston model and the market quotes for European-type options. By means of numerical experiments we show that our scheme enables a consistent and fast pricing of products that are sensitive to the forward volatility skew. Detailed error analysis is also provided.

Suggested Citation

  • Anthonie W. Van Der Stoep & Lech A. Grzelak & Cornelis W. Oosterlee, 2014. "The Heston Stochastic-Local Volatility Model: Efficient Monte Carlo Simulation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1-30.
  • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:07:n:s0219024914500459
    DOI: 10.1142/S0219024914500459
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    Citations

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    Cited by:

    1. Kaustav Das & Nicolas Langren'e, 2018. "Closed-form approximations with respect to the mixing solution for option pricing under stochastic volatility," Papers 1812.07803, arXiv.org, revised Mar 2020.
    2. Luca De Gennaro Aquino & Carole Bernard, 2019. "Semi-analytical prices for lookback and barrier options under the Heston model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 715-741, December.
    3. Daniel Guterding & Wolfram Boenkost, 2018. "The Heston stochastic volatility model with piecewise constant parameters - efficient calibration and pricing of window barrier options," Papers 1805.04704, arXiv.org, revised Jan 2019.
    4. Kaustav Das & Nicolas Langren'e, 2020. "Explicit approximations for option prices via Malliavin calculus for the stochastic Verhulst volatility model," Papers 2006.01542, arXiv.org.
    5. Ferreiro-Ferreiro, Ana María & García-Rodríguez, José A. & Souto, Luis & Vázquez, Carlos, 2020. "A new calibration of the Heston Stochastic Local Volatility Model and its parallel implementation on GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 467-486.
    6. Sergey Nasekin & Wolfgang Karl Hardle, 2020. "Model-driven statistical arbitrage on LETF option markets," Papers 2009.09713, arXiv.org.

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