A Comparison of Pricing Kernels for Garch Option Pricing With Generalized Hyperbolic Distributions

Abstract

Under discrete-time GARCH models markets are incomplete so there is more than one price kernel for valuing contingent claims. This motivates the quest for selecting an appropriate price kernel. Different methods have been proposed for the choice of a price kernel. Some of them can be justified by economic equilibrium arguments. This paper studies risk-neutral dynamics of various classes of Generalized Hyperbolic GARCH models arising from different price kernels. We discuss the properties of these dynamics and show that for some special cases, some pricing kernels considered here lead to similar risk neutral GARCH dynamics. Real data examples for pricing European options on the S&P 500 index emphasize the importance of the choice of a price kernel.

Non-Gaussian GARCH option pricing models and their diffusion limits

“…We use the NIG distribution as our candidate for the non-Gaussian driving noise. The pricing performance of threshold GARCH based option pricing models with NIG innovations (NIG-TGARCH) has been studied by Badescu et al (2011) for European style options or by Stentoft (2008) for American options, among others.…”

From Time Series of Returns to Option Prices: The Stochastic Discount Factor Approach

“…Nevertheless, it is important to remind that from P to Q em the only change is a shift in the conditional distributions, in particular, the conditional variance, the conditional skewness and the conditional kurtosis of the innovations remain constant. It may explain partly the poor pricing performances of this method for long maturity options as remarked in and Badescu et al (2011). The next method overcomes this empirical problem.…”

“…We refer the reader to Badescu et al (2009) for details. As in the Gaussian case (Proposition 3.2.3), it is sometimes possible (see Badescu et al , 2011 to relax the regression conditions for the aggregate consumption imposing a particular bivariate distribution for the pairs .Y t ; log.c t // or .Y t ; .c t //.…”

“…This is the point of view of Badescu et al (2011). The only difference between the two approaches is a modification in the parameterization of the model.…”

Testing for leverage effects in the returns of US equities

“…This article aims to provide a reliable measure of it using 25 years of S&P 500 returns. Following Badescu et al (2008Badescu et al ( , 2011 and Chorro et al (2010Chorro et al ( , 2012, we combine two classical asymmetric GARCH specifications used in the financial literature, namely, the Exponential GARCH (EGARCH) introduced by Nelson (1991) and the Asymmetric Power ARCH model (APARCH) of Ding et al (1993), with two families of conditional distributions that are able to generate various levels of skewness and kurtosis: the Generalized Hyperbolic distribution as introduced by Barndorff-Nielsen (1977) and the mixture of two Gaussian distributions (see e.g. Behboodian, 1970).…”