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Option Valuation in Multivariate SABR Models

Author

Listed:
  • Jörg Kienitz

    (Deutsche Postbank AG)

  • Manuel Wittke

    (University of Bonn)

Abstract

We consider the joint dynamic of a basket of n-assets where each asset itself follows a SABR stochastic volatility model. Using the Markovian Projection methodology we approximate a univariate displaced diffusion SABR dynamic for the basket to price caps and floors in closed form. This enables us to consider not only the asset correlation but also the skew, the cross-skew and the decorrelation in our approximation. The latter is not possible in alternative approximations to price e.g. spread options. We illustrate the method by considering the example where the underlyings are two constant maturity swap (CMS) rates. Here we examine the influence of the swaption volatility cube on CMS spread options and compare our approximation formulae to results obtained by Monte Carlo simulation and a copula approach.

Suggested Citation

  • Jörg Kienitz & Manuel Wittke, 2010. "Option Valuation in Multivariate SABR Models," Research Paper Series 272, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:272
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp272.pdf
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    Citations

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    Cited by:

    1. Kenichiro Shiraya & Akihiko Takahashi, 2012. "Pricing Multi-Asset Cross Currency Options," CARF F-Series CARF-F-290, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. A. M. Ferreiro & J. A. Garc'ia & J. G. L'opez-Salas & C. V'azquez, 2024. "SABR/LIBOR market models: pricing and calibration for some interest rate derivatives," Papers 2408.01470, arXiv.org.
    3. Cyril Grunspan, 2011. "A Note on the Equivalence between the Normal and the Lognormal Implied Volatility : A Model Free Approach," Papers 1112.1782, arXiv.org.
    4. Baaquie, Belal E. & Du, Xin & Bhanap, Jitendra, 2014. "Option pricing: Stock price, stock velocity and the acceleration Lagrangian," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 564-581.
    5. Kenichiro Shiraya & Akihiko Takahashi, 2012. "Pricing Multi-Asset Cross Currency Optionss," CIRJE F-Series CIRJE-F-844, CIRJE, Faculty of Economics, University of Tokyo.

    More about this item

    Keywords

    SABR; CMS spread; displaced diffusion; Markovian projection; Gyongy Lemma;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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