- Date: 20 Aug. (Thu.)
- Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
- Time: 16:50-18:20
- Speaker: Alex Novikov (University of Technology Sydney)
- Title: On calibration of diffusion processes: introduction to the general theory, the one‑dimensional case.
- Abstract:
We study the Maximum Likelihood Estimators (MLEs) of drift parameters in diffusion‑type models frequently deployed in quantitative finance.
The properties of these estimators are explored in the fixed‑horizon and sequential sampling schemes.
Extending the classical framework of Liptser–Shiryaev, we derive non‑asymptotic, semi‑analytic formulas for the moments of the MLEs
and establish their exponential boundedness.
We show that the bias and mean‑square error of the MLEs can be computed explicitly using integral‑transform techniques.
For ergodic diffusions, including Ornstein–Uhlenbeck and affine‑type processes, we demonstrate how to obtain exact numerical results
together with asymptotic expansions. We also discuss how these results may be adapted to high‑frequency discrete‑time observation schemes
relevant to financial data.
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