The Role of High Frequency Intra-Daily Data, Daily Range and Implied Volatility in Multi-Period Value-at-Risk Forecasting

Abstract

In this paper, we assess the informational content of daily range, realized variance, realized bipower variation, two time scale realized variance, realized range and implied volatility in daily, weekly, biweekly and monthly out-of-sample Value-at-Risk (VaR) predictions. We use the recently proposed Realized GARCH model combined with the skewed student distribution for the innovations process and a Monte Carlo simulation approach in order to produce the multi- Jel Classification: C13; C53; C58; G17; G21; G32

Option Pricing Under Time-Varying Risk-Aversion with Applications to Risk Forecasting

“…On the other hand, Brownless and Gallo [45] and Louzis et al [123] find that Value-at-Risk models based on realized volatility improve the forecasting performance considerably relative to GARCHtype Value-at-Risk models. 1 For more details about the Value-at-Risk see Chapter 6.5.2.…”

“…Giot [85]) or better (see e.g. Louzis et al [123]) than Value-at-Risk models based on historical information. More precisely, Giot [85] finds that Value-at-Risk forecasts based on Black-Scholes implied volatilities and GARCH-type models do have similar forecasting performance, even during challenging market conditions.…”

“…More precisely, Giot [85] finds that Value-at-Risk forecasts based on Black-Scholes implied volatilities and GARCH-type models do have similar forecasting performance, even during challenging market conditions. 2 Louzis et al [123] examine the forecasting performance of various Value-at-Risk models based on well established volatility forecasting methods, as for example option-implied volatilities or realized volatilities. Moreover, they make use of the recent developments in volatility forecasting, like the realized GARCH model of Hensen et al [91], which combines the GARCH model with realized volatility.…”

“…Moreover, they make use of the recent developments in volatility forecasting, like the realized GARCH model of Hensen et al [91], which combines the GARCH model with realized volatility. Louzis et al [123] find that no Value-at-Risk model based on historical data, neither daily nor intra-daily, can outperform Value-at-Risk models based on option-implied information, irrespective of the confidence level, forecasting horizon and evaluation metric.…”

“…3 The Value-at-Risk study of Louzis et al [123] is based on the S&P 500 index. Furthermore, Louzis et al [123] assume forecasting horizons of 1 day, 1, 2, 3, and 4 weeks, confidence levels of 95% and 99% as well as a skewed student's t distribution for the return innovations.…”