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Towards a $$\Delta $$Δ-Gamma Sato multivariate model

Author

Listed:
  • Lynn Boen

    (University of Antwerp)

  • Florence Guillaume

    (University of Antwerp)

Abstract

The increased trading in multi-name financial products has paved the way for the use of multivariate models that are at once computationally tractable and flexible enough to mimic the stylized facts of asset log-returns and of their dependence structure. In this paper we propose a new multivariate Lévy model, the so-called $$\varDelta $$Δ-Gamma model, where the log-price gains and losses are modeled by separate multivariate Gamma processes, each containing a common and an idiosyncratic component. Furthermore, we extend this multivariate model to the Sato setting, allowing for a moment term structure that is more in line with empirical evidence. We calibrate the two models on single-name option price surfaces and market implied correlations and we show how the $$\varDelta $$Δ-Gamma Sato model outperforms its Lévy counterpart, especially during periods of market turmoil. The numerical study also reveals the advantages of these new types of multivariate models, compared to a multivariate VG model.

Suggested Citation

  • Lynn Boen & Florence Guillaume, 2020. "Towards a $$\Delta $$Δ-Gamma Sato multivariate model," Review of Derivatives Research, Springer, vol. 23(1), pages 1-39, April.
    • Handle: RePEc:kap:revdev:v:23:y:2020:i:1:d:10.1007_s11147-019-09155-y
    DOI: 10.1007/s11147-019-09155-y
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Multi-name option pricing; Multivariate Lévy models; Multivariate models with Sato marginals; Difference of Gamma processes; Self-similar processes; Calibration;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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