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Multivariate Option Pricing with Time Varying Volatility and Correlations

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  • Jeroen V.K. Rombouts

    ()
    (Institute of Applied Economics at HEC Montréal, CIRANO, CIRPEE, Université catholique de Louvain (CORE))

  • Lars Stentoft

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

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.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2010-19.

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Length: 38
Date of creation: 30 Apr 2010
Date of revision:
Handle: RePEc:aah:create:2010-19

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Web page: http://www.econ.au.dk/afn/

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Keywords: Multivariate risk premia; Option pricing; GARCH models;

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Citations

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Cited by:
  1. Jeroen Rombouts & Lars Peter Stentoft & Francesco Violente, 2012. "The Value of Multivariate Model Sophistication: An Application to pricing Dow Jones Industrial Average Options," CIRANO Working Papers, CIRANO 2012s-05, CIRANO.
  2. Boyer, M. Martin & Stentoft, Lars, 2013. "If we can simulate it, we can insure it: An application to longevity risk management," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 35-45.
  3. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(3), pages 457-493, June.
  4. Donald Lien & Chongfeng Wu & Li Yang & Chunyang Zhou, 2013. "Dynamic and Asymmetric Dependences Between Chinese Yuan and Other Asia‐Pacific Currencies," Journal of Futures Markets, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 33(8), pages 696-723, 08.
  5. Beliaeva, Natalia & Nawalkha, Sanjay, 2012. "Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models," Journal of Banking & Finance, Elsevier, Elsevier, vol. 36(1), pages 151-163.
  6. Lars Stentoft, 2011. "What we can learn from pricing 139,879 Individual Stock Options," CREATES Research Papers, School of Economics and Management, University of Aarhus 2011-52, School of Economics and Management, University of Aarhus.
  7. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Kassberger, Stefan & Liebmann, Thomas, 2012. "When are path-dependent payoffs suboptimal?," Journal of Banking & Finance, Elsevier, Elsevier, vol. 36(5), pages 1304-1310.

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