Time-Changed Lévy Jump Processes with GARCH Model on Reverse Convertibles

Posted: 28 Oct 2012 Last revised: 1 May 2013

See all articles by Wei Simi, Ph.D.

Wei Simi, Ph.D.

City University of New York

Xiaoli Wang

Marist College - School of Management

Date Written: October 26, 2012

Abstract

Over decades, investors are more incline to pursue high-yield financial investment instruments at low interest rates economic environments. The increasing demand of high-yield products has given financial institutions the opportunities to create financial structured products. Reverse convertible notes are one of the kinds financial instruments and are high desired products in recent years started from Europe to the United States. The reverse convertible notes are complexes due to the notes are not plain bonds or stocks. They are structured products with embedded exotic equity options. Due to those unusual risks of reverse convertible notes, the general Black-Scholes option pricing model and a Compound Poisson Jump model that trying to catch large crashes are not suitable on pricing this kind of products. This paper proposes a new asset pricing framework by extending pure Brownian increments to Lévy Jump risks for stock returns movements to value reverse convertibles. It deals with time-changing volatilities of stock options with Lévy Jump processes by considering stock infinite-jump possibilities. It uses a discrete-time GARCH with time-varying dynamics Lévy Jump processes to stock’s return valuations. The results from the new model are closed to the market valuations, especially the Normal-Inverse-Gaussian model of the Lévy Jump family.

Keywords: Lévy Jump Process, Fourier transforms, exotic options, reverse convertible, stochastic volatility, GARCH

JEL Classification: G1, G2

Suggested Citation

Simi, Wei and Wang, Xiaoli, Time-Changed Lévy Jump Processes with GARCH Model on Reverse Convertibles (October 26, 2012). Review of Financial Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2167512 or http://dx.doi.org/10.2139/ssrn.2167512

Wei Simi (Contact Author)

City University of New York ( email )

New York, NY
United States

Xiaoli Wang

Marist College - School of Management ( email )

United States

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