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Covariance dependent kernels, a Q-affine GARCH for multi-asset option pricing

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  • Escobar-Anel, Marcos
  • Rastegari, Javad
  • Stentoft, Lars

Abstract

This paper introduces a class of multivariate GARCH models that extends the existing literature by explicitly modeling correlation dependent pricing kernels. A large subclass admits closed-form recursive solutions for the moment generating function under the risk-neutral measure, which permits efficient pricing of multi-asset options. We perform a full calibration to three bivariate series of index returns and their corresponding volatility indexes in a joint maximum likelihood estimation. The results empirically confirm the presence of correlation dependance in addition to the well known variance dependance in the pricing kernel. The model improves both the overall likelihood and the VIX-implied likelihoods, with a better fitting of marginal distributions, e.g., 15% less error on one-asset option prices. The new degree of freedom is also shown to significantly impact the shape of marginal and joint pricing kernels, and leads to up to 53% differences for out-of-the-money two-asset correlation option prices.

Suggested Citation

  • Escobar-Anel, Marcos & Rastegari, Javad & Stentoft, Lars, 2023. "Covariance dependent kernels, a Q-affine GARCH for multi-asset option pricing," International Review of Financial Analysis, Elsevier, vol. 87(C).
    • Handle: RePEc:eee:finana:v:87:y:2023:i:c:s1057521923001382
    DOI: 10.1016/j.irfa.2023.102622
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    References listed on IDEAS

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    More about this item

    Keywords

    Pricing; Multi-asset options; GARCH models; Closed form solutions; Covariance dependent kernel; Maximum likelihood estimation;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • 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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