TY - JOUR
T1 - Saddlepoint approximations for continuous-time Markov processes
AU - Aït-Sahalia, Yacine
AU - Yu, Jialin
N1 - Funding Information:
We are grateful to the Editor and two anonymous referees for their comments. This research was funded in part by the NSF under Grant SES-0111140.
PY - 2006/10
Y1 - 2006/10
N2 - 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.
AB - 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.
KW - Characteristic function
KW - Closed-form approximation
KW - Infinitesimal generator
KW - Transition density
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U2 - 10.1016/j.jeconom.2005.07.004
DO - 10.1016/j.jeconom.2005.07.004
M3 - Article
AN - SCOPUS:33747883866
SN - 0304-4076
VL - 134
SP - 507
EP - 551
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 2
ER -