Summary: Journal of Econometrics 134 (2006) 507551
Saddlepoint approximations for continuous-time
Yacine Ai¨t-Sahaliaa,Ã, Jialin Yub
Department of Economics, Princeton University and NBER, Princeton, NJ 08544, USA
Department of Finance and Economics, Columbia University, New York, NY 10027, USA
Available online 30 August 2005
This paper proposes saddlepoint expansions as a means to generate closed-form
approximations to the transition densities and cumulative distribution functions of Markov
processes. This method is applicable to a large class of models considered in finance, for which
a Laplace or characteristic functions, but not the transition density, can be found in closed
form. But even when such a computation is not possible explicitly, we go one step further by
showing how useful approximations can be obtained by replacing the Laplace or characteristic
functions by an expansion in small time.
r 2005 Elsevier B.V. All rights reserved.
JEL classification: C13; C22; C32
Keywords: Transition density; Infinitesimal generator; Characteristic function; Closed-form