Louis Arsenault - Mahjoubi
Title: Applications of nonlinear non-Gaussian deterministic filters in finance
Date: May 28th, 2026
Time: 9:40am
Location: LIB 2020/ Zoom
Supervised by: Jean-Fran莽ois B茅gin
Abstract:
Deterministic filtering algorithms are powerful tools to estimate models with latent stochastic processes. This thesis presents three applications of discrete nonlinear filtering (DNF) algorithms to stochastic volatility (SV) models in finance. The first is the SVDNF R package, an open-source implementation of the DNF for several commonly-used SV models, enabling users to create custom models with key features such as leverage effects, return and volatility discontinuities. The second project applies the DNF to accurately estimating financial alpha in the context of asset pricing models. The alpha estimate can be contaminated by two sources of model misspecification: unmodelled systematic risk factors and improper error specifications. We combine the DNF with Markov chain Monte Carlo for Bayesian model estimation and use predictive model stacking to account for model uncertainty. We then fit several popular asset pricing models with both homoscedastic errors and SV. In empirical applications (e.g., factor-spanning regression tests, market-anomaly identification, equity alpha estimation), we obtain significantly different alpha estimates when stacking across various model sets, suggesting that model uncertainty is an important consideration when estimating alpha. The last project addresses a particular weakness of the DNF: numerical integration suffers from the curse of dimensionality.We present an integration-by-parts filter (IBPF) with a better quadrature error convergence rate than standard DNF integration. Moreover, we derive a numerical integration grid using a grid-thinning scheme where the number of integration points required is in a lower computational complexity class than standard product integration methods. We present derivations for the IBPF and grid-thinning scheme, examine their theoretical properties (i.e., convergence rates), test their effectiveness in simulation, and estimate a novel discrete-time SV model with jumps and multiple latent processes using the proposed methods. We find that the more complex model specifications better fit market data.