Generalized Pareto Processes and Liquidity

TL;DR

This paper introduces new time series models with generalized Pareto marginals to better capture liquidity risk in fund management, providing theoretical properties, estimation methods, and real-world application insights.

Contribution

It proposes novel ARGP-based models tailored for liquidity data, establishing their statistical properties and demonstrating their effectiveness with empirical fund redemption data.

Findings

Models accurately capture liquidity risk features.

Estimation methods are consistent and asymptotically normal.

Models fit real-world fund redemption data well.

Abstract

Motivated by the modeling of liquidity risk in fund management in a dynamic setting, we propose and investigate a class of time series models with generalized Pareto marginals: the autoregressive generalized Pareto process (ARGP), a modified ARGP (MARGP) and a thresholded ARGP (TARGP). These models are able to capture key data features apparent in fund liquidity data and reflect the underlying phenomena via easily interpreted, low-dimensional model parameters. We establish stationarity and ergodicity, provide a link to the class of shot-noise processes, and determine the associated interarrival distributions for exceedances. Moreover, we provide estimators for all relevant model parameters and establish consistency and asymptotic normality for all estimators (except the threshold parameter, which as usual must be dealt with separately). Finally, we illustrate our approach using real-world fund redemption data, and we discuss the goodness-of-fit of the estimated models.