Jump-Diffusion Models with Correlated Brownian Motion and Compound Poisson Processes

30 Pages Posted: 14 Nov 2010

See all articles by Weiping Li

Weiping Li

Civil Aviation Flight University of China ; Oklahoma State University

Timothy L. Krehbiel

Oklahoma State University, Stillwater

Date Written: September 24, 2010

Abstract

In this paper we provide a closed form option pricing model with underlying uncertainty modeled as an exponential Lévy process. The stochastic structure of our model relaxes the restrictive assumption of zero covariance between the Brownian motion and Poisson process jump size found in all traditional jump-diffusion models. The resulting equity diffusion and jump risk premia of the equilibrium consumption capital asset pricing relationship are non-linear functions of time. The option pricing model is developed using Rubinstein’s method of pricing by substitution in equilibrium and it is shown that the sign and magnitude of this covariance plays a crucial role in determining the slope of the implied volatility term structure.

Suggested Citation

Li, Weiping and Krehbiel, Timothy L., Jump-Diffusion Models with Correlated Brownian Motion and Compound Poisson Processes (September 24, 2010). Available at SSRN: https://ssrn.com/abstract=1708320 or http://dx.doi.org/10.2139/ssrn.1708320

Weiping Li (Contact Author)

Civil Aviation Flight University of China ( email )

46 Nanchang road
Guanghan, Sichuan 618307
China

Oklahoma State University ( email )

Stillwater, OK
United States

Timothy L. Krehbiel

Oklahoma State University, Stillwater ( email )

Stillwater, OK 74078-0555
United States

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