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Hybrid Lévy Models: Design and Computational Aspects

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  • Ernst Eberlein
  • Marcus Rudmann

Abstract

A hybrid model is a model, where two markets are studied jointly such that stochastic dependence can be taken into account. Such a dependence is well known for equity and interest rate markets on which we focus here. Other pairs can be considered in a similar way. Two different versions of a hybrid approach are developed. Independent time-inhomogeneous Lévy processes are used as the drivers of the dynamics of interest rates and equity. In both versions, the dynamics of the interest rate side is described by an equation for the instantaneous forward rate. Dependence between the markets is generated by introducing the driver of the interest rate market as an additional term into the dynamics of equity in the first version. The second version starts with the equity dynamics and uses a corresponding construction for the interest rate side. Dependence can be quantified in both cases by a single parameter. Numerically efficient valuation formulas for interest rate and equity derivatives are developed. Using market quotes for liquidly traded assets we show that the hybrid approach can be successfully calibrated.

Suggested Citation

  • Ernst Eberlein & Marcus Rudmann, 2018. "Hybrid Lévy Models: Design and Computational Aspects," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(5-6), pages 533-556, November.
    • Handle: RePEc:taf:apmtfi:v:25:y:2018:i:5-6:p:533-556
    DOI: 10.1080/1350486X.2018.1536523
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    Cited by:

    1. Ballotta, Laura & Eberlein, Ernst & Schmidt, Thorsten & Zeineddine, Raghid, 2021. "Fourier based methods for the management of complex life insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 320-341.
    2. Kira Henshaw & Cedric H. A. Koffi & Olivier Menoukeu Pamen & Raghid Zeineddine, 2024. "On the valuation of life insurance policies for dependent coupled lives," Papers 2410.11849, arXiv.org.

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