A Note on the Wang Transform for Stochastic Volatility Pricing Models

14 Pages Posted: 18 Oct 2015 Last revised: 29 Jul 2016

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: October 16, 2015

Abstract

In this paper we study a conditional version of the Wang transform in the context of discrete GARCH models and their diffusion limits. Our first contribution shows that the conditional Wang transform and Duan’s generalized local risk-neutral valuation relationship based on equilibrium considerations, lead to the same GARCH option pricing model. We derive the weak limit of an asymmetric GARCH model risk-neutralized via Wang's transform. The connection with stochastic volatility limits constructed using other standard pricing kernels, such as the conditional Esscher transform or the extended Girsanov principle, is further investigated by comparing the corresponding market prices of variance risk.

Keywords: distortion function, stochastic discount factor, generalized local risk-neutral valuation relationship, GARCH models, weak convergence, stochastic volatility

JEL Classification: C22, C32, C5

Suggested Citation

Badescu, Alex and Cui, Zhenyu and Ortega, Juan-Pablo, A Note on the Wang Transform for Stochastic Volatility Pricing Models (October 16, 2015). Available at SSRN: https://ssrn.com/abstract=2675308

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

Paper statistics

Downloads
70
Rank
274,685
Abstract Views
264