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Option Valuation with IG-GARCH Model and an U-Shaped Pricing Kernel

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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

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  • Christophe Chorro & Fanirisoa Rahantamialisoa H., 2016. "Option Valuation with IG-GARCH Model and an U-Shaped Pricing Kernel," Documents de travail du Centre d'Economie de la Sorbonne 16074, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:16074
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    Keywords

    Option valuation; Pricing kernel; VIX; IG-GARCH; S&P500;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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