Saddlepoint Approximations for Affine Jump-Diffusion Models

Posted: 8 Oct 2008

See all articles by Paul Glasserman

Paul Glasserman

Columbia Business School

Kyoung-Kuk Kim

Korea Advanced Institute of Science and Technology

Date Written: March 2008


Affine jump-diffusion (AJD) processes constitute a large and widely used class of continuous-time asset pricing models that balance tractability and flexibility in matching market data. The prices of e.g., bonds, options, and other assets in AJD models are given by extended pricing transforms that have an exponential-affine form; these transforms have been characterized in great generality by Duffie, Pan and Singleton [28]. Calculating model prices requires inversion of these transforms, and this has limited the application of AJD models to the comparatively small subclass for which the transforms are available in closed form. This article seeks to widen the scope of AJD models amenable to practical application through approximate transform inversion techniques. More specifically, we develop the use of saddlepoint approximations for AJD models. These approximations facilitate the calculation of prices in AJD models whose transforms are not available explicitly. We derive and test several alternative saddlepoint approximations and find that they produce accurate prices over a wide range of parameters.

Keywords: Transform inversion, Characteristic function, Option prices, Numerical approximations

JEL Classification: C13, C32, C49

Suggested Citation

Glasserman, Paul and Kim, Kyoung-Kuk, Saddlepoint Approximations for Affine Jump-Diffusion Models (March 2008). Journal of Economic Dynamics and Control, Forthcoming, Available at SSRN:

Paul Glasserman

Columbia Business School ( email )

3022 Broadway
403 Uris Hall
New York, NY 10027
United States
212-854-4102 (Phone)
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Kyoung-Kuk Kim (Contact Author)

Korea Advanced Institute of Science and Technology ( email )

Dept of Industrial and Systems Engineering
Daejeon, 305-701
Korea, Republic of (South Korea)

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