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

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.