Forecasting Intraday Volatility and Value-at-Risk with High-Frequency Data

In this paper, we develop modeling tools to forecast Value-at-Risk and volatility with investment horizons of less than one day. We quantify the market risk based on the study at a 30-min time horizon using modified GARCH models. The evaluation of intraday market risk can be useful to market participants (day traders and market makers) involved in frequent trading. As expected, the volatility features a significant intraday seasonality, which motivates us to include the intraday seasonal indexes in the GARCH models. We also incorporate realized variance (RV) and time-varying degrees of freedom in the GARCH models to capture more intraday information on the volatile market. The intrinsic tail risk index is introduced to assist with understanding the inherent risk level in each trading time interval. The proposed models are evaluated based on their forecasting performance of one-period-ahead volatility and Intraday Value-at-Risk (IVaR) with application to the 30 constituent stocks. We find that models with seasonal indexes generally outperform those without; RV can improve the out-of-sample forecasts of IVaR; student GARCH models with time-varying degrees of freedom perform best at 0.5 and 1 % IVaR, while normal GARCH models excel for 2.5 and 5 % IVaR. The results show that RV and seasonal indexes are useful to forecasting intraday volatility and Intraday VaR.     

FORECASTING VOLATILITY FOR PORTFOLIO SELECTION

The volatility of an asset is a primary input to the portfolio selection problem. Information about volatility is available from two sources, namely the share market and the option market. This paper examines the forecasting performance, over a three month investment horizon, of time series forecasts (from the share market) and option based implied volatilities. Three time series models, including GARCH, are used and twenty four implied volatility estimation models are employed. Using a data set of twelve UK companies, it is demonstrated that implied volatilities produce better individual forecasts than time series. However, more remarkably, forecasts combining implied volatilies and time series estimates significantly outperform both component forecasts.     

Forecasting daily variability of the S&P 100 stock index using historical,realised and implied volatility measurements

The increasing availability of financial market data at intraday frequencies has not only led to the development of improved volatility measurements but has also inspired research into their potential value as an information source for volatility forecasting. In this paper, we explore the forecasting value of historical volatility (extracted from daily return series), of implied volatility (extracted from option pricing data) and of realised volatility (computed as the sum of squared high frequency returns within a day). First, we consider unobserved components (UC-RV) and long memory models for realised volatility which is regarded as an accurate estimator of volatility. The predictive abilities of realised volatility models are compared with those of stochastic volatility (SV) models and generalised autoregressive conditional heteroskedasticity (GARCH) models for daily return series. These historical volatility models are extended to include realised and implied volatility measures as explanatory variables for volatility. The main focus is on forecasting the daily variability of the Standard & Poor's 100 (S&P 100) stock index series for which trading data (tick by tick) of almost 7 years is analysed. The forecast assessment is based on the hypothesis of whether a forecast model is outperformed by alternative models. In particular, we will use superior predictive ability tests to investigate the relative forecast performances of some models. Since volatilities are not observed, realised volatility is taken as a proxy for actual volatility and is used for computing the forecast error. A stationary bootstrap procedure is required for computing the test statistic and its p-value. The empirical results show convincingly that realised volatility models produce far more accurate volatility forecasts compared to models based on daily returns. Long memory models seem to provide the most accurate forecasts.     

Forecasting Commodity Market Returns Volatility: A Hybrid Ensemble Learning GARCH-LSTM based Approach

This study investigates the advantage of combining the forecasting abilities of multiple generalized autoregressive conditional heteroscedasticity (GARCH)-type models, such as the standard GARCH (GARCH), exponential GARCH (eGARCH), and threshold GARCH (tGARCH) models with advanced deep learning methods to predict the volatility of five important metals (nickel, copper, tin, lead, and gold) in the Indian commodity market. This paper proposes integrating the forecasts of one to three GARCH-type models into an ensemble learning-based hybrid long short-term memory (LSTM) model to forecast commodity price volatility. We further evaluate the forecasting performance of these models for standalone LSTM and GARCH-type models using the root mean squared error, mean absolute error, and mean fundamental percentage error. The results highlight that combining the information from the forecasts of multiple GARCH types into a hybrid LSTM model leads to superior volatility forecasting capability. The SET-LSTM, which represents the model that combines forecasts of the GARCH, eGARCH, and tGARCH into the LSTM hybrid, has shown the best overall results for all metals, barring a few exceptions. Moreover, the equivalence of forecasting accuracy is tested using the Diebold–Mariano and Wilcoxon signed-rank tests.     

Forecasting volatility of crude oil futures using a GARCH–RNN hybrid approach

Volatility is an important element for various financial instruments owing to its ability to measure the risk and reward value of a given financial asset. Owing to its importance, forecasting volatility has become a critical task in financial forecasting. In this paper, we propose a suite of hybrid models for forecasting volatility of crude oil under different forecasting horizons. Specifically, we combine the parameters of generalized autoregressive conditional heteroscedasticity (GARCH) and Glosten–Jagannathan–Runkle (GJR)-GARCH with long short-term memory (LSTM) to create three new forecasting models named GARCH–LSTM, GJR-LSTM, and GARCH-GJRGARCH LSTM in order to forecast crude oil volatility of West Texas Intermediate on different forecasting horizons and compare their performance with the classical volatility forecasting models. Specifically, we compare the performances against existing methodologies of forecasting volatility such as GARCH and found that the proposed hybrid models improve upon the forecasting accuracy of Crude Oil: West Texas Intermediate under various forecasting horizons and perform better than GARCH and GJR-GARCH, with GG–LSTM performing the best of the three proposed models at 7-, 14-, and 21-day-ahead forecasts in terms of heteroscedasticity-adjusted mean square error and heteroscedasticity-adjusted mean absolute error, with significance testing conducted through the model confidence set showing that GG–LSTM is a strong contender for forecasting crude oil volatility under different forecasting regimes and rolling-window schemes. The contribution of the paper is that it enhances the forecasting ability of crude oil futures volatility, which is essential for trading, hedging, and purposes of arbitrage, and that the proposed model dwells upon existing literature and enhances the forecasting accuracy of crude oil volatility by fusing a neural network model with multiple econometric models.     

Forecasting Value-at-Risk using high frequency data: The realized range model

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.     

Forecasting hedge fund volatility: a Markov regime-switching approach

The article addresses forecasting volatility of hedge fund (HF) returns by using a non-linear Markov-Switching GARCH (MS-GARCH) framework. The in- and out-of-sample, multi-step ahead volatility forecasting performance of GARCH(1,1) and MS-GARCH(1,1) models is compared when applied to 12 global HF indices over the period of January 1990 to October 2010. The results identify different regimes with periods of high and low volatility for most HF indices. In-sample estimation results reveal a superior performance of the MS-GARCH model. The findings show that regime switching is related to structural changes in the market factor for most strategies. Out-of-sample forecasting shows that the MS-GARCH formulation provides more accurate volatility forecasts for most forecast horizons and for most HF strategies. Inclusion of MS dynamics in the GARCH specification highly improves the volatility forecasts for those strategies that are particularly sensitive to general macroeconomic conditions, such as Distressed Restructuring and Merger Arbitrage.     

Financial crisis,Value-at-Risk forecasts and the puzzle of dependency modeling

Forecasting Value-at-Risk (VaR) for financial portfolios is a crucial task in applied financial risk management. In this paper, we compare VaR forecasts based on different models for return interdependencies: volatility spillover (Engle & Kroner, 1995), dynamic conditional correlations (Engle, 2002, 2009) and (elliptical) copulas (Embrechts et al., 2002). Moreover, competing models for marginal return distributions are applied. In particular, we apply extreme value theory (EVT) models to GARCH-filtered residuals to capture excess returns.Drawing on a sample of daily data covering both calm and turbulent market phases, we analyze portfolios consisting of German Stocks, national indices and FX-rates. VaR forecasts are evaluated using statistical backtesting and Basel II criteria. The extensive empirical application favors the elliptical copula approach combined with extreme value theory (EVT) models for individual returns. 99% VaR forecasts from the EVT-GARCH-copula model clearly outperform estimates from alternative models accounting for dynamic conditional correlations and volatility spillover for all asset classes in times of financial crisis.     

Are RiskMetrics forecasts good enough? Evidence from 31 stock markets

Academic research has highlighted the inherent flaws within the RiskMetrics model and demonstrated the superiority of the GARCH approach in-sample. However, these results do not necessarily extend to forecasting performance. This paper seeks answer to the question of whether RiskMetrics volatility forecasts are adequate in comparison to those obtained from GARCH models. To answer the question stock index data is taken from 31 international markets and subjected to two exercises, a straightforward volatility forecasting exercise and a Value-at-Risk exceptions forecasting competition. Our results provide some simple answers to the above question. When forecasting volatility of the G7 stock markets the APARCH model, in particular, provides superior forecasts that are significantly different from the RiskMetrics models in over half the cases. This result also extends to the European markets with the APARCH model typically preferred. For the Asian markets the RiskMetrics model performs well, and is only significantly dominated by the GARCH models for one market, although there is evidence that the APARCH model provides a better forecast for the larger Asian markets. Regarding the Value-at-Risk exercise, when forecasting the 1% VaR the RiskMetrics model does a poor job and is typically the worst performing model, again the APARCH model does well. However, forecasting the 5% VaR then the RiskMetrics model does provide an adequate performance. In short, the RiskMetrics model only performs well in forecasting the volatility of small emerging markets and for broader VaR measures.     

预测中国宏观经济变量:专家与模型的组合预测

本文使用组合预测方法,探究以“朗润预测”为代表的专家预测以及计量模型对于中国宏观经济变量的预测效果,并研究对不同预测进行组合预测是否有助于改进预测效果。本文发现,对我国CPI和GDP的增长率,专家预测效果总体上优于模型预测。从原因看,一方面,专家在预测时已经考虑了计量模型的预测信息;另一方面,在经济出现“拐点”的时期,专家通过对实际经济环境和政策的把握,得出更准确的经济预测。组合预测有助于提升预测精度,对专家预测进行组合得到的预测效果优于大多数的专家预测,“模型—专家”组合预测的效果也优于所有的模型和大部分专家预测。     

On the Predictability of the Stock Market Volatility: Does History Matter?

This study compares the performance of the ISD, the GARCH (1,1) , the historical volatility estimates and of two lagged trading volume measures for predicting the Swiss Stock Market Index's (SMI) volatility. The ISD has a superior daily informational content than the GARCH (1,1) estimate and retains unbiased but decreasing explanatory power over up to 20 days ahead horizons. Mean and spread daily volume measures play a significant correcting role when forecasting stock market volatility over daily and longer intervals respectively and clearly dominate the GARCH (1,1) forecasts. Their significance emphasises heterogeneous horizon traders' influence on the SMI volatility time series properties     

PREDICTING SYSTEMATIC RISK WITH MACROECONOMIC AND FINANCIAL VARIABLES

We analyze the predictive power of several macroeconomic and financial indicators in forecasting quarterly realized betas of 30 industry and 25 size and book-to-market portfolios. We model realized betas as autoregressive processes of order 1 and include lagged values of macroeconomic and financial indicators as exogenous predictor variables. In out-of-sample forecasting exercises, forecasts using bond market variables as exogenous predictors statistically outperform forecasts from a benchmark model without any exogenous predictors. These forecasts based on bond market variables also economically outperform benchmark forecasts by providing better performance in hedging the market risk of portfolios.     

Financial turbulence,systemic risk and the predictability of stock market volatility

This paper adds a novel perspective to the literature by exploring the predictive performance of two relatively unexplored indicators of financial conditions, i.e. financial turbulence and systemic risk, over stock market volatility using a sample of seven emerging and advanced economies. The two financial indicators that we utilize in our predictive setting provide a unique perspective on market conditions, as they relate directly to portfolio performance metrics from both volatility and co-movement perspectives and, unlike other macro-financial indicators of uncertainty, or risk, can be integrated into diversification models within forecasting and portfolio design settings. Since the data for the two predictors are available at a weekly frequency, and our focus is to produce forecasts at the daily frequency, we use the generalized autoregressive conditional heteroskedasticity-mixed data sampling (GARCH-MIDAS) approach. The results suggest that incorporating the two financial indicators (singly and jointly) indeed improves the out-of-sample predictive performance of stock market volatility models over both the short and long horizons. We observe that the financial turbulence indicator that captures asset price deviations from historical patterns does a better job when it comes to the out-of-sample prediction of future returns compared with the measure of systemic risk, captured by the absorption ratio. The outperformance of the financial turbulence indicator implies that unusual deviations in not only asset returns, but also in correlation patterns play a role in the persistence of return volatility. Overall, the findings provide an interesting opening for portfolio design purposes, in that financial indicators, which are directly associated with portfolio diversification performance metrics, can also be utilized for forecasting purposes, with significant implications for dynamic portfolio allocation strategies.     

A Comparison of Alternative Forecast Models of REIT Volatility

This study compares the relative performance of several well-known models in the forecasting of REIT volatility. Overall our results suggest that long-memory models (ARFIMA & FIGARCH) provide the best forecasts. Using either a large sample or some statistically justified small subsamples, we find that long memory models consistently outperform their short-memory counterparts (GARCH & Stochastic Volatility models) over a variety of forecast horizons. We also find that asymmetric models (EGARCH & FIEGARCH) are the worst performers among all models. Our study complements and extends a recent study of Cotter and Stevenson (2008) which demonstrates the usefulness of long-memory models in modeling REIT volatility. We conclude that in addition to modeling REIT volatility, long-memory models should also be adopted to forecast REIT volatility.     

Stock market volatility: Identifying major drivers and the nature of their impact

Financial-market risk, commonly measured in terms of asset-return volatility, plays a fundamental role in investment decisions, risk management and regulation. In this paper, we investigate a new modeling strategy that helps to better understand the forces that drive market risk. We use componentwise gradient boosting techniques to identify financial and macroeconomic factors influencing volatility and to assess the specific nature of their influence. Componentwise boosting is capable of producing parsimonious models from a, possibly, large number of predictors and—in contrast to other related techniques—allows a straightforward interpretation of the parameter estimates.Considering a wide range of potential risk drivers, we apply boosting to derive monthly volatility predictions for the equity market represented by S&P 500 index. Comparisons with commonly-used GARCH and EGARCH benchmark models show that our approach substantially improves out-of-sample volatility forecasts for short- and longer-run horizons. The results indicate that risk drivers affect future volatility in a nonlinear fashion.     

Interpreting financial market crashes as earthquakes: A new Early Warning System for medium term crashes

We propose a modeling framework which allows for creating probability predictions on a future market crash in the medium term, like sometime in the next five days. Our framework draws upon noticeable similarities between stock returns around a financial market crash and seismic activity around earthquakes. Our model is incorporated in an Early Warning System for future crash days. Testing our EWS on S&P 500 data during the recent financial crisis, we find positive Hanssen–Kuiper Skill Scores. Furthermore our modeling framework is capable of exploiting information in the returns series not captured by well known and commonly used volatility models. EWS based on our models outperform EWS based on the volatility models forecasting extreme price movements, while forecasting is much less time-consuming.     

Forecasting volatility of the U.S. oil market

We examine the information content of the CBOE Crude Oil Volatility Index (OVX) when forecasting realized volatility in the WTI futures market. Additionally, we study whether other market variables, such as volume, open interest, daily returns, bid-ask spread and the slope of the futures curve, contain predictive power beyond what is embedded in the implied volatility. In out-of-sample forecasting we find that econometric models based on realized volatility can be improved by including implied volatility and other variables. Our results show that including implied volatility significantly improves daily and weekly volatility forecasts; however, including other market variables significantly improves daily, weekly and monthly volatility forecasts.     

Volatility forecasting of crude oil futures market: Which structural change-based HAR models have better performance?

The paper focuses on the smooth and sharp structural changes in crude oil futures volatility and singles out the flexible Fourier form (FFF) and the modified ICSS algorithm to detect them, respectively, so as to explore whether different structural change-based HAR models exhibit significantly better performance for crude oil return volatility forecasting than traditional HAR-type models. The empirical results indicate that, on the one hand, crude oil market displays a strong evidence of breaks, and the incorporation of trigonometric terms can account for the structural changes in crude oil return volatility. On the other hand, the flexible Fourier form (FFF) based HAR-type models and the Structural Breakpoints (SB) based HAR-type models yield superior forecasting performance than traditional HAR-type models. Meanwhile, the forecasting results and economic performance of the former usually outperform the latter, particularly for the short- and medium-term forecasts.     

Robust outlier detection for Asia–Pacific stock index returns

Outliers can lead to model misspecifications, poor forecasts and invalid inferences. Their identification and correction is therefore an important objective of financial modeling.This paper introduces a simple method to detect outliers in a financial series. It uses an AR(1)–GARCH(1,1) model to calculate interval forecasts for one-step ahead returns that are then compared to realized returns to determine whether or not we are in the presence of an aberrant observation. The GARCH model, however, is only used as a filter and the identification algorithm remains robust to model misspecifications.The efficiency of this outlier-correction technique is first tested with a simulation study, before being applied to five Asian stock market returns to identify the outlying observations. After an analysis of these extreme fluctuations, the out-of-sample forecasting performance of our outlier-corrected model is then compared to the classical forecasts of a GARCH model in which no account is taken of outliers.     

基于实现极差和实现波动率的中国金融市场风险测度研究

目前比较流行的金融市场风险价值研究一般采用日收益数据,并基于GARCH类模型进行估计和预测。本文利用沪深股指日内高频数据,分别通过ARFIMA模型和CARR模型对实现波动率和较新的实现极差建模,计算风险价值。通过对VaR的似然比和动态分位数等回测检验,实证分析了各种模型的VaR预测能力。结果显示,使用日内高频数据的实现波动率和实现极差模型的预测能力强于采用日数据的各种GARCH类模型。