A Random Holding Period Approach for Liquidity-Inclusive Risk Management

Abstract

Within the context of risk integration, we introduce 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 in 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 nonlinear 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 SHPs appears to be unfeasible. We finally discuss potential developments following future availability of market data. This chapter is a refined version of the original working paper by Brigo and Nordio (2010) [14].