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Multivariate option pricing with time varying volatility and correlations

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  • ROMBOUTS, Jeroen J. K

    (Institute of Applied Economics at HEC Montréal, CIRANO, CIRPEE, Montréal (QC), Canada; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • STENTOFT, Lars

    (Department of Finance at HEC Montréal, CIRANO, CIRPEE, CREATES, Montréal (QC), Canada)

Abstract

In recent years multivariate models for asset returns have received much attention, in particular this is the case for models with time varying volatility. In this paper we consider models of this class and examine their potential when it comes to option pricing. Specifically, we derive the risk neutral dynamics for a general class of multivariate heteroskedastic models, and we provide a feasible way to price options in this framework. Our framework can be used irrespective of the assumed underlying distribution and dynamics, and it nests several important special cases. We provide an application to options on the minimum of two indices. Our results show that not only is correlation important for these options but so is allowing this correlation to be dynamic. Moreover, we show that for the general model exposure to correlation risk carries an important premium, and when this is neglected option prices are estimated with errors. Finally, we show that when neglecting the non-Gaussian features of the data, option prices are also estimated with large errors.

Suggested Citation

  • ROMBOUTS, Jeroen J. K & STENTOFT, Lars, 2010. "Multivariate option pricing with time varying volatility and correlations," LIDAM Discussion Papers CORE 2010020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2010020
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      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    8. Rombouts, Jeroen V.K. & Stentoft, Lars, 2015. "Option pricing with asymmetric heteroskedastic normal mixture models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 635-650.
    9. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(3), pages 457-493, June.
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    15. Xiaochuan Pang & Shushang Zhu & Xueting Cui & Jiali Ma, 2022. "Systemic Risk of Optioned Portfolios: Controllability and Optimization," Papers 2209.04685, arXiv.org.
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    18. Trucíos, Carlos & Hotta, Luiz K. & Valls Pereira, Pedro L., 2019. "On the robustness of the principal volatility components," Journal of Empirical Finance, Elsevier, vol. 52(C), pages 201-219.
    19. Lars Stentoft, 2013. "American option pricing using simulation with an application to the GARCH model," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 5, pages 114-147, Edward Elgar Publishing.
    20. Fang Liang & Lingshan Du & Zhuo Huang, 2023. "Option pricing with overnight and intraday volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(11), pages 1576-1614, November.
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    More about this item

    Keywords

    multivariate risk premia; option pricing; GARCH models;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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