Jump liquidity risk and its impact on CVaR

Purpose – The aim is to study jump liquidity risk and its impact on risk measures: value at risk (VaR) and conditional VaR (CVaR). Design/methodology/approach – The liquidity discount factor is modelled with mean revision jump diffusion processes and the liquidity risk is integrated in the framework of VaR and CVaR. Findings – The standard VaR, CVaR, and the liquidity adjusted VaR can seriously underestimate the potential loss over a short holding period for rare jump liquidity events. A better risk measure is the liquidity adjusted CVaR which gives a more realistic loss estimation in the presence of the liquidity risk. An efficient Monte Carlo method is also suggested to find approximate VaR and CVaR of all percentiles with one set of samples from the loss distribution, which applies to portfolios of securities as well as single securities. Originality/value – The paper offers plausible stochastic processes to model liquidity risk.