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Option Valuation with IG_GARCH Model and an U-Shaped Pricing Kernel

Author

Listed:
  • Christophe Chorro

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Fanirisoa Rahantamialisoa H.

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Dipartimento di Economia [Venezia] - University of Ca’ Foscari [Venice, Italy])

Abstract

Empirical and theoretical studies have attempted to establish the U-shape of the log-ratio of conditional risk-neutral and physical probability density functions. The main subject of this paper is to question the use of such a U-shaped pricing kernel to improve option pricing performances. Starting from the so-called Inverse Gaussian GARCH model (IG-GARCH), known to provide semi-closed form formulas for classical European derivatives when an exponential affine pricing kernel is used, we build a new pricing kernel that is non-monotonic and that still has this remarkable property. Using a daily dataset of call options written on the S&P500 index, we compare the pricing performances of these two IG-GARCH models proving, in this framework, that the new exponential U-shaped stochastic discount factor clearly outperforms the classical exponential affine one. What is more, several estimation strategies including options or VIX information are tested taking advantage of the analytical tractability of these models.

Suggested Citation

  • Christophe Chorro & Fanirisoa Rahantamialisoa H., 2016. "Option Valuation with IG_GARCH Model and an U-Shaped Pricing Kernel," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01400242, HAL.
    • Handle: RePEc:hal:cesptp:halshs-01400242
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01400242
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    Cited by:

    1. Alexandru Badescu & Zhenyu Cui & Juan-Pablo Ortega, 2019. "Closed-form variance swap prices under general affine GARCH models and their continuous-time limits," Annals of Operations Research, Springer, vol. 282(1), pages 27-57, November.

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