Mixed-frequency quantile regression with realized volatility to forecast Value-at-Risk (original) (raw)
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Mixed-frequency quantile regressions to forecast value-at-risk and expected shortfall
Annals of Operations Research
Although quantile regression to calculate risk measures is widely established in the financial literature, when considering data observed at mixed-frequency, an extension is needed. In this paper, a model is built on a mixed-frequency quantile regressions to directly estimate the Value-at-Risk (VaR) and the Expected Shortfall (ES) measures. In particular, the low-frequency component incorporates information coming from variables observed at, typically, monthly or lower frequencies, while the high-frequency component can include a variety of daily variables, like market indices or realized volatility measures. The conditions for the weak stationarity of the daily return process are derived and the finite sample properties are investigated in an extensive Monte Carlo exercise. The validity of the proposed model is then explored through a real data application using two energy commodities, namely, Crude Oil and Gasoline futures. Results show that our model outperforms other competing s...
Using Mixed-Frequency and Realized Measures in Quantile Regression
2020
Quantile regression is an efficient tool when it comes to estimate popular measures of tail risk such as the conditional quantile Value at Risk. In this paper we exploit the availability of data at mixed frequency to build a volatility model for daily returns with low-- (for macro--variables) and high--frequency (which may include an \virg{--X} term related to realized volatility measures) components. The quality of the suggested quantile regression model, labeled MF--Q--ARCH--X, is assessed in a number of directions: we derive weak stationarity properties, we investigate its finite sample properties by means of a Monte Carlo exercise and we apply it on financial real data. VaR forecast performances are evaluated by backtesting and Model Confidence Set inclusion among competitors, showing that the MF--Q--ARCH--X has a consistently accurate forecasting capability.
Forecasting Value-at-Risk using nonlinear regression quantiles and the intra-day range
International Journal of Forecasting, 2012
Value-at-Risk (VaR) is commonly used for financial risk measurement. It has recently become even more important, especially during the 2008-09 global financial crisis. We propose some novel nonlinear threshold conditional autoregressive VaR (CAViaR) models that incorporate intra-day price ranges. Model estimation and inference are performed using the Bayesian approach via the link with the Skewed-Laplace distribution. We examine how a range of risk models perform during the 2008-09 financial crisis, and evaluate how the crisis affects the performance of risk models via forecasting VaR. Empirical analysis is conducted on five Asia-Pacific Economic Cooperation stock market indices as well as two exchange rate series. We examine violation rates, back-testing criteria, market risk charges and quantile loss function values to measure and assess the forecasting performance of a variety of risk models. The proposed threshold CAViaR model, incorporating range information, is shown to forecast VaR more efficiently than other models, across the series considered, which should be useful for financial practitioners.
Forecasting Value-at-Risk using high frequency data: The realized range model
Global Finance Journal, 2009
Current studies on financial market risk measures usually use daily returns based on GARCH type models. This paper models realized range using intraday high frequency data based on CARR framework and apply it to VaR forecasting. Kupiec LR test and dynamic quantile test are used to compare the performance of VaR forecasting of realized range model with another intraday realized volatility model and daily GARCH type models. Empirical results of Chinese Stock Indices show that realized range model performs the same with realized volatility model, which performs much better than daily models.
2005
This paper employs a new approach due to in order to examine market risk in several major equity markets, as well as for major companies listed in New York Stock Exchange and Athens Stock Exchange. By interpreting the VaR as the quantile of future portfolio values conditional on current information, propose a new approach to quantile estimation that does not require any of the extreme assumptions of the existing methodologies, mainly normality and i.i.d. returns. The CAViaR model shifts the focus of attention from the distribution of returns directly to the behaviour of the quantile. We provide a comparative evaluation of the predictive performance of four alternative CAViaR specifications, namely Adaptive, Symmetric Absolute Value, Asymmetric Slope and Indirect GARCH(1,1) models. The main findings of the present analysis is that we are able to confirm some stylized facts of financial data such as volatility clustering while the Dynamic Quantile criterion selects different models for different confidence intervals for the case of the five general indices, the US companies and the Greek companies respectively.
Quantile Autoregression and its application to Financial Risk Management and Portfolio Optimization
2014
Increasing globalization, complexity of capital markets and the expanding range of exotic financial instruments have made financial risk management difficult to evaluate. As a consequence, a rise in use of more sophisticated risk management systems has not led to better results. Most financial data exhibits time varying volatility and heavy tails therefore an appropriate risk measure should capture these features. Volatility patterns reflect different characteristics in different stock markets. The main aim of this study is to improve on volatility estimation by use of Quantile Autoregression frameworks. To avoid strong assumptions about the form of innovations, an initial proxy of volatility estimator is proposed. The estimator is assumed to capture the intraday volatility based on the conditional Interquantile Autoregressive Range. A class of a-mixing time series models based on quantile regression are used and direct estimation of coefficients as introduced by Koenker and Bassett...
Studies in Nonlinear Dynamics & Econometrics, 2018
Risk measures such as value-at-risk (VaR) and expected shortfall (ES) may require the calculation of quantile functions from quantile regression models. In a parametric set-up, we propose to regress directly on the quantiles of a distribution and demonstrate a method through the conditional autoregressive range model which has increasing popularity in recent years. Two flexible distribution families: the generalised beta type two on positive support and the generalised-t on real support (which requires log transformation) are adopted for the range data. Then the models are extended to allow the volatility dynamic and compared in terms of goodness-of-fit. The models are implemented using the module fmincon in Matlab under the classical likelihood approach and applied to analyse the intra-day high-low price ranges from the All Ordinaries index for the Australian stock market. Quantiles and upper-tail conditional expectations evaluated via VaR and ES respectively are forecast using the...
Nucleus, 2017
Risk by Regression Quantiles (CAViaR) model. The CAViaR model interprets the Value-at-Risk (VaR) as the quantile of future portfolio values conditional on current information and directly compute this quantile instead of inverting the distribution of returns. An asymmetric conditional heteroscedastic specification for CAViaR is proposed and applied along with four commonly used CAViaR specifications for the one-dayahead VaR estimation of KSE for the period 1998-2010. The in-sample and out-of-sample predictive performance of alternative CAViaR specifications are compared and evaluated. The proposed model that accounts for asymmetry of risk is found to produce better and reliable estimates for VaR of KSE.