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Liquidity-adjusted Market Risk Measures with Stochastic Holding Period

by Damiano Brigo of King's College, London, and
Claudio Nordio of Banco Popolare, Milan

October 20, 2010

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.

JEL Classification: C15, C16, G10, G18.

AMS Classification: 62G32, 91B28, 91B70.

Keywords: Liquidity Risk, Random Holding Period, Systemic Risk, Basel Agreement, Value at Risk, Expected Shortfall, Stochastic Holding Period, Variance Normal Mixture, Tail Dependence, Heavy Tailed Distributions, Kendall's tau.

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