Option valuation with IG-GARCH model and a U-shaped pricing kernel

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.

VIX futures pricing with conditional skewness

“…The main results of Table 14 are as follows: First, the average annualized volatility of the S&P 500 returns is higher than the average annualized volatility reported in Table 2. We find a similarly high average annualized volatility in Chorro and Fanirisoa (2016) when they jointly fit the S&P 500 returns and the VIX.…”

Discriminating Between GARCH Models for Option Pricing by Their Ability to Compute Accurate VIX Measures

“…One important aspect of our empirical study will be to question once again this duality. Following Kanniainen et al (2014) we choose the widely recognized NGARCH Engle & Ng (1993), GJR-GARCH Glosten et al (1993), and affine HN- GARCH Heston & Nandi (2000) models and we add the IG-GARCH of Christoffersen et al (2006a) (see also Chorro & Fanirisoa (2019)) that is a notable example of an affine model within a non-Gaussian setting. In the next sections we briefly recall the definitions and the main properties of these specifications.…”

“…Based on this result, Kanniainen et al (2014) proposed a fair comparison between affine and non-affine Gaussian GARCH specifications using log-returns and VIX information in the estimation. 5 For two affine GARCH models Chorro & Fanirisoa (2019) and Papantonis (2016) proved that incorporating both the physical return dynamics of the index and risk-neutral dynamics of the VIX to estimate the parameters of GARCH option pricing models provides competitive pricing errors at a very low computational cost. 6 This paper attempts to fill several gaps in the GARCH option pricing literature, in particular, from an empirical point of view.…”

“…As a natural non-Gaussian alternative we favor the so-called NIG distribution not only because it is known to fit statistical properties of asset returns remarkably but also because, combined with Esscher and EGP SDF, pricing equations may be solved explicitly. 8 Furthermore, monotonic and non-monotonic pricing kernels (Monfort & Pégoraro (2012) and Chorro & Fanirisoa (2019)) are considered for Gaussian and IG distributions.…”

“…To our knowledge, in the existing literature, empirical studies questioned, in general, the impact of the distribution (Christoffersen et al (2006a), Chorro et al (2012)), the choice of the SDF (Badescu et al (2011), Christoffersen et al (2013), Chorro & Fanirisoa (2019)) or the estimation strategy ( Hao & Zhang (2013), Kanniainen et al (2014), Papantonis (2016), Lalancette & Simonato (2017)) on pricing performances, but none of them consider all these factors at the same time. For example, in Christoffersen et al (2004) and Kanniainen et al (2014) the authors study different GARCH structures with different estimation strategies, but restrict themselves to the Gaussian setting while in Chorro & Fanirisoa (2019) the authors focus on different SDF and estimation strategies only for the IG-GARCH model. Our study is a means of making a contribution to understand the combined impact of these complementary aspects (21 combinations of GARCH-distribution-SDF-estimation are tested), instead of providing restrictive pairwise comparisons, and to conclude that the combination of all them is fundamental to producing competitive valuation errors.…”