Liquidity-adjusted Intraday Value at Risk Modeling and Risk Management: an Application to Data from Deutsche Börse

Abstract

This paper develops a high-frequency risk measure, the Liquidity-adjusted Intraday Value at Risk (LIVaR). Our objective is to explicitly consider the endogenous liquidity dimension associated with order size. Taking liquidity into consideration when using intraday data is important because significant position changes over very short horizons may have large impacts on stock returns. By reconstructing the open Limit Order Book (LOB) of Deutsche Börse, the changes of tick-by-tick ex-ante frictionless return and actual return are modeled jointly using a Log-ACD-VARMA-MGARCH structure. This modeling helps to identify the dynamics of frictionless and actual returns, and to quantify the risk related to the liquidity premium. From a practical perspective, our model can be used not only to identify the impact of ex-ante liquidity risk on total risk, but also to provide an estimation of VaR for the actual return at a point in time. In particular, there will be considerable time saved in constructing the risk measure for the waiting cost because once the models have been identified and estimated, the risk measure over any time horizon can be obtained by simulation without re-sampling the data and re-estimating the model.