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Extension of stochastic volatility equity models with the Hull--White interest rate process

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  • Lech A. Grzelak
  • Cornelis W. Oosterlee
  • Sacha Van Weeren

Abstract

We present an extension of stochastic volatility equity models by a stochastic Hull--White interest rate component while assuming non-zero correlations between the underlying processes. We place these systems of stochastic differential equations in the class of affine jump-diffusion--linear quadratic jump-diffusion processes so that the pricing of European products can be efficiently performed within the Fourier cosine expansion pricing framework. We compare the new stochastic volatility Schöbel--Zhu--Hull--White hybrid model with a Heston--Hull--White model, and also apply the models to price hybrid structured derivatives that combine the equity and interest rate asset classes.

Suggested Citation

  • Lech A. Grzelak & Cornelis W. Oosterlee & Sacha Van Weeren, 2012. "Extension of stochastic volatility equity models with the Hull--White interest rate process," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 89-105, July.
    • Handle: RePEc:taf:quantf:v:12:y:2012:i:1:p:89-105
    DOI: 10.1080/14697680903170809
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    References listed on IDEAS

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    1. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    2. Fang, Fang & Oosterlee, Kees, 2008. "Pricing Early-Exercise and Discrete Barrier Options by Fourier-Cosine Series Expansions," MPRA Paper 9248, University Library of Munich, Germany.
    3. Alan L. Lewis, 2001. "A Simple Option Formula for General Jump-Diffusion and other Exponential Levy Processes," Related articles explevy, Finance Press.
    4. Roger Lord & Christian Kahl, 2006. "Why the Rotation Count Algorithm works," Tinbergen Institute Discussion Papers 06-065/2, Tinbergen Institute.
    5. Gaspar, Raquel M., 2004. "General Quadratic Term Structures of Bond, Futures and Forward Prices," SSE/EFI Working Paper Series in Economics and Finance 559, Stockholm School of Economics.
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