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Non-Affine GARCH Option Pricing Models, Variance Dependent Kernels, and Diffusion Limits

54 Pages Posted: 19 Dec 2015 Last revised: 12 Jun 2017

Alex Badescu

University of Calgary

Zhenyu Cui

Stevens Institute of Technology

Juan-Pablo Ortega

Universität Sankt Gallen; Centre National de la Recherche Scientifique (CNRS)

Date Written: December 18, 2015

Abstract

This paper investigates the pricing and weak convergence of an asymmetric non-affine, non-Gaussian GARCH model when the risk-neutralization is based on a variance dependent exponential linear pricing kernel with stochastic risk aversion parameters. The risk-neutral dynamics are obtained for a general setting and its weak limit is derived. We show how several GARCH diffusions, martingalized via well-known pricing kernels, are obtained as special cases and we derive necessary and sufficient conditions for the presence of financial bubbles. An extensive empirical analysis using both historical returns and options data illustrates the advantage of coupling this pricing kernel with non-Gaussian innovations.

Keywords: non-affine GARCH models, non-Gaussian innovations, exponential linear variance dependent pricing kernel, bivariate diffusion limit, option pricing

JEL Classification: C58, G12, G13

Suggested Citation

Badescu, Alex and Cui, Zhenyu and Ortega, Juan-Pablo, Non-Affine GARCH Option Pricing Models, Variance Dependent Kernels, and Diffusion Limits (December 18, 2015). Available at SSRN: https://ssrn.com/abstract=2705324 or http://dx.doi.org/10.2139/ssrn.2705324

Alex Badescu

University of Calgary ( email )

University of Calgary
Calgary, Alberta
Canada

Zhenyu Cui

Stevens Institute of Technology ( email )

School of Business
Castle Point in the Hudson
Hoboken, NJ 07030
United States
(201) 216-3726 (Phone)

HOME PAGE: http://sites.google.com/site/zhenyucui86/

Juan-Pablo Ortega (Contact Author)

Universität Sankt Gallen ( email )

Bodanstrasse 6
St. Gallen, St. Gallen CH-9000
Switzerland

HOME PAGE: http://juan-pablo-ortega.com

Centre National de la Recherche Scientifique (CNRS) ( email )

16 route de Gray
Besançon, 25030
France

HOME PAGE: http://juan-pablo-ortega.com

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