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

Christophe Chorro () and Fanirisoa Rahantamialisoa H. ()
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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]

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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.

Keywords: Option valuation; Pricing kernel; VIX; IG-GARCH; S&P 500 (search for similar items in EconPapers)
Date: 2016-11
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01400242
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Published in 2016

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