Liquidity Adjusted Value at Risk: Integrating the Uncertainty in Depth and Tightness

Abstract

Efficient market risk management should also focus on the market liquidity risk, which is generally ignored by the conventional Value at Risk Metrics. We propose two alternative parametric methods to existing studies for the estimation of Liquidity Adjusted Value at Risk (LVaR). The first model is based on the volatility dynamics of VNET (Engle and Lange, 2001) whereas the second model also incorporates the first two moments of the tightness dimension to the latter, as measured by relative weighted bid-ask spreads. Considering a portfolio with different underlying volatility assumptions (EWMA, GARCH-CCC, GARCH-DCC), validation results indicate that both parametric LVaR approaches are strong alternatives to tightness based LVaR models and strictly superior to conventional VaR models, with respect to performance related to regulatory compliance, statistical coverage and overall relative cost of liquidity vs. loss size on violation days.