Analytical Option Pricing Under an Asymmetrically Displaced Double Gamma Jump-Diffusion Model

48 Pages Posted: 18 Aug 2013 Last revised: 12 Feb 2018

See all articles by Matthias Thul

Matthias Thul

IMC Financial Markets

Ally Zhang

Department of Finance, Lancaster University Management School; Swiss Finance Institute

Date Written: May 1, 2014

Abstract

We generalize the Kou (2002) double exponential jump-diffusion model in two directions. First, we independently displace the two tails of the jump size distribution away from the origin. Second, we allow for each of the displaced tails to follow a gamma distribution with an integer-valued shape parameter. Both extensions introduce additional flexibility in the tails of the corresponding return distribution. Our model is supported by an equilibrium economy and we obtain closed-form solutions for European plain vanilla options. Our valuation function is computationally fast to evaluate and robust across the full parameter space. We estimate the physical model parameters through maximum likelihood and for a diverse sample of equities, commodities and exchange rates. For all assets under consideration, the original Kou (2002) model can be rejected in favor of our newly introduced asymmetrically displaced double gamma dynamics.

Keywords: displaced tails, jump-diffusion, option pricing, maximum likelihood estimation

JEL Classification: C13, G13

Suggested Citation

Thul, Matthias and Zhang, Quan, Analytical Option Pricing Under an Asymmetrically Displaced Double Gamma Jump-Diffusion Model (May 1, 2014). 26th Australasian Finance and Banking Conference 2013; Swiss Finance Institute Research Paper No. 17-78. Available at SSRN: https://ssrn.com/abstract=2311673 or http://dx.doi.org/10.2139/ssrn.2311673

Matthias Thul (Contact Author)

IMC Financial Markets ( email )

Strawinskylaan 377, WTC D-tower
Amsterdam, 1077 XX
Netherlands

Quan Zhang

Department of Finance, Lancaster University Management School ( email )

Economics Department,
LUMS,
Bailrigg Lancaster, LA1 4YX
United Kingdom
+441524592776 (Phone)

HOME PAGE: http://www.allyquanzhang.com/wordpress/

Swiss Finance Institute ( email )

Plattenstrasse 32
Zurich, ZH 8032
Switzerland

Register to save articles to
your library

Register

Paper statistics

Downloads
233
rank
123,640
Abstract Views
1,349
PlumX Metrics