A multimodal asymmetric exponential power distribution: Application to risk measurement for financial high-frequency data

Abstract

Interest in risk measurement for high-frequency data has increased since the volume of high-frequency trading stepped up over the two last decades. This paper proposes a multimodal extension of the Exponential Power Distribution (EPD), called the Multimodal Asymmetric Exponential Power Distribution (MAEPD). We derive moments and we propose a convenient stochastic representation of the MAEPD. We establish consistency, asymptotic normality and efficiency of the maximum likelihood estimators (MLE). An application to risk measurement for high-frequency data is presented. An autoregressive moving average multiplicative component generalized autoregressive conditional heteroskedastic (ARMA-mcsGARCH) model is fitted to Financial Times Stock Exchange (FTSE) 100 intraday returns. Performances for Value-at-Risk (VaR) and Expected Shortfall (ES) estimation are evaluated. We show that the MAEPD outperforms commonly used distributions in risk measurement.