Risk Model Validation: An Intraday VaR and ES Approach Using the Multiplicative Component GARCH

Ravi Summinga-Sonagadu,Jason Narsoo

doi:10.3390/risks7010010

Abstract

In this paper, we employ 99% intraday value-at-risk (VaR) and intraday expected shortfall (ES) as risk metrics to assess the competency of the Multiplicative Component Generalised Autoregressive Heteroskedasticity (MC-GARCH) models based on the 1-min EUR/USD exchange rate returns. Five distributional assumptions for the innovation process are used to analyse their effects on the modelling and forecasting performance. The high-frequency volatility models were validated in terms of in-sample fit based on various statistical and graphical tests. A more rigorous validation procedure involves testing the predictive power of the models. Therefore, three backtesting procedures were used for the VaR, namely, the Kupiec’s test, a duration-based backtest, and an asymmetric VaR loss function. Similarly, three backtests were employed for the ES: a regression-based backtesting procedure, the Exceedance Residual backtest and the V-Tests. The validation results show that non-normal distributions are best suited for both model fitting and forecasting. The MC-GARCH(1,1) model under the Generalised Error Distribution (GED) innovation assumption gave the best fit to the intraday data and gave the best results for the ES forecasts. However, the asymmetric Skewed Student’s-t distribution for the innovation process provided the best results for the VaR forecasts. This paper presents the results of the first empirical study (to the best of the authors’ knowledge) in: (1) forecasting the intraday Expected Shortfall (ES) under different distributional assumptions for the MC-GARCH model; (2) assessing the MC-GARCH model under the Generalised Error Distribution (GED) innovation; (3) evaluating and ranking the VaR predictability of the MC-GARCH models using an asymmetric loss function.

Highlights

Since the financial crisis of 2008, there has been an ever-growing need for financial entities to accurately assess their exposure to financial risks
This paper presents the results of the first empirical study in: (1) forecasting the intraday Expected Shortfall (ES) under different distributional assumptions for the MC-GARCH model; (2) assessing the MC-GARCH model under the Generalised Error Distribution (GED) innovation; (3) evaluating and ranking the VaR
This study focuses on forecasting the intraday Value-at-Risk (VaR) and intraday Expected Shortfall (ES) at 99% confidence level using the MC-GARCH model under five distributional assumptions

Summary

Introduction

Since the financial crisis of 2008, there has been an ever-growing need for financial entities to accurately assess their exposure to financial risks. Risk being commonly characterised by increasing volatility in the financial market, the modelling and forecasting of the volatility have become a very important research area among academics and practitioners in the last decade. According to Poon and Granger (2001), volatility can be viewed as a ‘barometer for the vulnerability of financial markets and the economy’. It is, important to forecast volatility accurately. Volatility is an essential tool in the computation of other risk metrics such as Value-at-Risk (VaR) and Expected Shortfall (ES). Value-at-Risk (VaR) is a mandatory risk management tool in the insurance and banking industry as per the regulatory norms of the Solvency II framework (Solvency II European Directive (2009/138/EC))

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Conclusion