| | |
Summary: Telling from Discrete Data Whether
the Underlying Continuous-Time
Model Is a Diffusion
YACINE AÏT-SAHALIA*
ABSTRACT
Can discretely sampled financial data help us decide which continuous-time mod-
els are sensible? Diffusion processes are characterized by the continuity of their
sample paths. This cannot be verified from the discrete sample path: Even if the
underlying path were continuous, data sampled at discrete times will always ap-
pear as a succession of jumps. Instead, I rely on the transition density to determine
whether the discontinuities observed are the result of the discreteness of sampling,
or rather evidence of genuine jump dynamics for the underlying continuous-time
process. I then focus on the implications of this approach for option pricing models.
IN MANY INSTANCES IN FINANCIAL ECONOMETRICS, we make inference about a pos-
tulated continuous-time model on the basis of discretely sampled observa-
tions. Among potential continuous-time models, most specifications adopted
have been diffusions, although the literature is more and more frequently
allowing for jumps ~see Merton ~1976!, Ahn and Thompson ~1988!, Bates
~1991!, Das and Foresi ~1996!, Duffie, Pan, and Singleton ~2000!, Aït-
Sahalia, Wang, and Yared ~2001!, among others!.
|
