Columbia & NYU Financial Engineering Colloquium: Xin Guo, Agostino Caponi, & Rama Cont

Agostino Capponi

Professor
Department of Industrial Engineering and Operations Research
Columbia University

Title

Data-Driven Dynamic Factor Modeling via Manifold Learning

Abstract

We propose a data-driven dynamic factor framework where a response variable $y(t) \in \mathbb{R}^m$ depends on a high-dimensional set of covariates $x(t) \in \mathbb{R}^d$ without imposing any parametric model on the joint covariate dynamics. Leveraging diffusion maps - a nonlinear manifold learning technique introduced in Coifman and Lafon [2006] - our framework uncovers the joint dynamics of the covariates in a purely data-driven way. It achieves this by constructing lower-dimensional covariate embeddings that retain most of the explanatory power for the time series of responses $y(t)$, while exhibiting simple linear dynamics. We combine diffusion maps with Kalman filtering techniques to infer the latent dynamic covariate embeddings, and predict the response variable directly from the diffusion map embedding space.

We apply the framework to stress testing equity portfolios using a combination of financial and macroeconomic factors from the FED's supervisory scenarios. Unlike standard scenario analysis (SSA), where one assumes that the conditional expectation of the unstressed factors given the scenario is zero, we account for dynamic correlation between stressed and unstressed risk factors through a novel conditional sampling procedure. We demonstrate that our data-driven stress testing procedure outperforms SSA- and PCA-based benchmarks through historical backtests spanning three major financial crises, achieving reductions in mean absolute error (MAE) of up to 52\% and 57\% for scenario-based portfolio return prediction, respectively. (joint work with Graeme Baker and Jose Sidaoui Gali).

More details to come on Xin Guo & Rama Cont.