Deep Learning in Finance – Lecture 3
Speaker: Prof. Ovidiu Calin, Eastern Michigan University
Host: S Baskar
Title: Learning Stochastic Processes Part I: Calibration
Time, day and date: 5:00:00 PM – 6:00:00 PM, Tuesday, August 11
Venue: Ramanujan Hall
Abstract: This presentation introduced modern approaches for learning and calibrating stochastic processes from data using machine learning. Beginning with Gaussian processes, we showed how neural networks can be used to approximate the time-dependent mean and variance functions, transforming the observations into a standardized process that should follow a standard normal distribution. This viewpoint naturally leads to calibration methods based on quantile matching, which compare the entire empirical distribution rather than only its first moments, providing a more robust alternative to classical moment-matching techniques. We then extended the framework to learning covariance kernels, enabling the recovery of temporal dependence in Gaussian processes, with simplified formulations for stationary models. The second part focused on the calibration of stochastic differential equations, using the Langevin (Ornstein–Uhlenbeck) process as a representative example. After deriving its explicit solution and statistical properties, we discussed several calibration strategies, including moment matching, quantile matching, and autoregressive estimation. Throughout the presentation, neural-network-based calibration was presented as a flexible and powerful alternative to traditional estimation methods, capable of learning unknown statistical quantities directly from observed trajectories while providing a unified framework applicable to a broad class of stochastic models encountered in finance, physics, engineering, and data science.