Liquidity-adjusted Market Risk Measures with Stochastic Holding Period

TL;DR

This paper introduces stochastic holding period models to create liquidity-adjusted market risk measures, capturing market liquidity effects and tail risks without fixed time horizons, using mixture distributions and dependence structures.

Contribution

It proposes a novel framework for risk measurement incorporating stochastic holding periods, allowing for skewness, heavy tails, and dependence modeling in liquidity-adjusted risk assessment.

Findings

Mixture distributions can model skewness and heavy tails in returns.

Dependent SHP processes may induce tail dependence among assets.

Increasing dependence via common SHPs is challenging to achieve.

Abstract

Within the context of risk integration, we introduce in risk measurement stochastic holding period (SHP) models. This is done in order to obtain a `liquidity-adjusted risk measure' characterized by the absence of a fixed time horizon. The underlying assumption is that - due to changes on market liquidity conditions - one operates along an `operational time' to which the P&L process of liquidating a market portfolio is referred. This framework leads to a mixture of distributions for the portfolio returns, potentially allowing for skewness, heavy tails and extreme scenarios. We analyze the impact of possible distributional choices for the SHP. In a multivariate setting, we hint at the possible introduction of dependent SHP processes, which potentially lead to non linear dependence among the P&L processes and therefore to tail dependence across assets in the portfolio, although this may require drastic choices on the SHP distributions. We also find that increasing dependence as measured by Kendall's tau through common SHP's appears to be unfeasible. We finally discuss potential developments following future availability of market data.