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Stochastic covariance and dimension reduction in the pricing of basket options

Author

Listed:
  • Marcos Escobar

    () (Ryerson University)

  • Daniel Krause

    () (Technische Universität München)

  • Rudi Zagst

    () (Technische Universität München)

Abstract

Abstract This paper presents a tailor-made method for dimension reduction aimed at approximating the price of basket options in the context of stochastic volatility and stochastic correlation. The methodology is built on a modification to the Principal Component Stochastic Volatility (PCSV) model, a stochastic covariance model that accounts for most stylized facts in prices. The method to reduce dimension is first derived theoretically. Afterwards the results are applied to a multivariate lognormal context as a special case of the PCSV model. Finally empirical results for the application of the method to the general PCSV model are illustrated.

Suggested Citation

  • Marcos Escobar & Daniel Krause & Rudi Zagst, 2016. "Stochastic covariance and dimension reduction in the pricing of basket options," Review of Derivatives Research, Springer, vol. 19(3), pages 165-200, October.
  • Handle: RePEc:kap:revdev:v:19:y:2016:i:3:d:10.1007_s11147-016-9119-x
    DOI: 10.1007/s11147-016-9119-x
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    References listed on IDEAS

    as
    1. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. C. Gourieroux, 2006. "Continuous Time Wishart Process for Stochastic Risk," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 177-217.
    4. repec:wsi:ijtafx:v:14:y:2011:i:06:n:s0219024911006784 is not listed on IDEAS
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    More about this item

    Keywords

    Principal components; Basket options; Stochastic covariance;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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