Modeling Liquidity Impact on Volatility: A GARCH-FunXL Approach

Abstract

We introduce a new semiparametric model, GARCH with Functional EXogeneous Liquidity (GARCH-FunXL), to capture the impact of liquidity, as implied by a stock exchange’s complete electronic limit order book (LOB), on asset price volatility. LOB-implied liquidity can be viewed as a functional rather than scalar or vectorial stochastic process. We adopt ideas from the functional data analysis (FDA) literature to link scalar conditional return volatility to curve-valued liquidity. Simulation experiments for a log-GARCH version of the model show that it works well in finite samples. Applying our new methodology to intraday return data from the German XETRA system, we find a substantial liquidity impact on return variation. Finally, we show that the forecast performance of the GARCH-FunXL model is clearly superior as compared to a model without liquidity impact.