April 15 at 4 pm (CEST).
Presenters: Blanka Horvath and Issa Zacharia (King’s College London)
Title: An Optimal Transport Approach to Market Regime Clustering
Abstract: The problem of rapid and automated detection of distinct market regimes is a topic of great interest to financial mathematicians and practitioners alike. In this paper, we outline an unsupervised learning algorithm clusters a given time-series – corresponding to an asset or index – into a suitable number of temporal segments (market regimes). This method – the principle of which is inspired by the well-known k-means algorithm – clusters said segments on the space of probability measures with finite p-th moment. On this space, our choice of metric is the p-Wasserstein distance. We compare our Wasserstein-kmeans approach with a more traditional implementation of the kmeans algorithm by generating clusters in Euclidean space via the first N raw moments of each log-return segment instead (moment-kmeans). We compare the two approaches initially on real data and validate the performance of either algorithm by studying the maximum mean discrepancy between, and within, clusters. We show that the Wasserstein-kmeans algorithm vastly outperforms the moment-based approach on both real and synthetic data. In particular, the Wasserstein-kmeans algorithm performs well, even when the distribution associated to each regime is non-Gaussian.