Saddlepoint approximations for affine jump-diffusion models

Abstract

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 et al. [2000. Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68, 1343–1376]. 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.