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Analytical option pricing under an asymmetrically displaced double gamma jump-diffusion model


Thul, Matthias; Zhang, Ally Quan (2014). Analytical option pricing under an asymmetrically displaced double gamma jump-diffusion model. Social Science Research Network 2311673, University of Zurich.

Abstract

We generalize the Kou (2002) double exponential jump-diusion 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 exibility 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.

We generalize the Kou (2002) double exponential jump-diusion 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 exibility 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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
JEL Classification:C13, G13
Language:English
Date:2014
Deposited On:03 Mar 2014 10:07
Last Modified:05 Apr 2016 17:44
Series Name:Social Science Research Network
Number of Pages:46
Additional Information:26th Australasian Finance and Banking Conference 2013
Official URL:http://ssrn.com/abstract=2311673
Other Identification Number:merlin-id:8902
Permanent URL: https://doi.org/10.5167/uzh-93715

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