Clustering of discretely observed diffusion processes

TL;DR

This paper introduces a novel dissimilarity measure for clustering diffusion processes observed discretely, effectively capturing differences in drift and diffusion coefficients in financial data.

Contribution

It proposes a new quadratic distance based on estimated Markov operators that does not require shrinking observation meshes, improving clustering of asset dynamics.

Findings

Effective in distinguishing drift and diffusion differences

Works well on synthetic and real stock data

Outperforms traditional metrics in capturing process differences

Abstract

In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time. The mesh of observations is not required to shrink to zero. As distance between two observed paths, the quadratic distance of the corresponding estimated Markov operators is considered. Analysis of both synthetic data and real financial data from NYSE/NASDAQ stocks, give evidence that this distance seems capable to catch differences in both the drift and diffusion coefficients contrary to other commonly used metrics.