Telling from Discrete Data Whether the Underlying Continuous-Time Model Is a Diffusion


  • Yacine Aït-Sahalia

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    • Aït-Sahalia is with the Department of Economics and the Bendheim Center for Finance, Princeton University and NBER. I am grateful to the editor and the referee, as well as Robert Bliss; Halyna Frydman; Lars Hansen; Samuel Karlin; Huston McCulloch; Chris Rogers; and Jim Stock for helpful discussions and comments; and to seminar participants at the American Mathematical Society, Berkeley, Cornell, the Econometric Society, the Federal Reserve Bank of Atlanta, the Fields Institute in Mathematical Sciences, the Institute of Mathematical Statistics, LSE, the NBER Summer Institute, NYU, Ohio State, Stanford, ULB, the University of Chicago, the University of Illinois, the University of Iowa, UNC Chapel Hill, the University of Washington, Vanderbilt, the Western Finance Association, and Wharton. Financial support from an Alfred P. Sloan Research Fellowship and the NSF (Grant SES-9996023) is gratefully acknowledged. Some of the material contained here circulated previously in a draft under the title “Do interest rates really follow continuous-time diffusions?”


Can discretely sampled financial data help us decide which continuous-time models 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 appear 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.