Forecasting volatility

In this paper, we investigate the time series properties of S&P 100 volatility and the forecasting performance of different volatility models. We consider several nonparametric and parametric volatility measures, such as implied, realized and model‐based volatility, and show that these volatility processes exhibit an extremely slow mean‐reverting behavior and possible long memory. For this reason, we explicitly model the near‐unit root behavior of volatility and construct median unbiased forecasts by approximating the finite‐sample forecast distribution using bootstrap methods. Furthermore, we produce prediction intervals for the next‐period implied volatility that provide important information about the uncertainty surrounding the point forecasts. Finally, we apply intercept corrections to forecasts from misspecified models which dramatically improve the accuracy of the volatility forecasts. Copyright © 2006 John Wiley & Sons, Ltd.     

Comparison of Realized Measure and Implied Volatility in Forecasting Volatility

This paper compares the information content of realized measures constructed from high‐frequency data and implied volatilities from options in the context of forecasting volatility. The comparison is based on within‐sample and out‐of‐sample (over horizons of 1–22 days) forecasts of daily S&P 500 index return volatility. The paper adds to the findings of previous studies, by considering recent developments in the related practice and the literature. It is shown that, for within‐sample fitting, the realized measure is more informative than the implied volatility. In contrast, the implied volatility is more informative than the realized measure for out‐of‐sample forecasting, in particular for multi‐step‐ahead forecasting. Moreover, we show that it is helpful to use all the information provided by the realized measure and the implied volatility for the within‐sample fitting. For multi‐step‐ahead forecasting, however, it is better to use only the implied volatility. Copyright © 2013 John Wiley & Sons, Ltd.     

Forecasting exchange rate volatility: a multiple horizon comparison using historical,realized and implied volatility measures

Recent studies suggest realized volatility provides forecasts that are as good as option‐implied volatilities, with improvement stemming from the use of high‐frequency data instead of a long‐memory specification. This paper examines whether volatility persistence can be captured by a longer dataset consisting of over 15 years of intra‐day data. Volatility forecasts are evaluated using four exchange rates (AUD/USD, EUR/USD, GBP/USD, USD/JPY) over horizons ranging from 1 day to 3 months, using an expanded set of short‐range and long‐range dependence models. The empirical results provide additional evidence that significant incremental information is found in historical forecasts, beyond the implied volatility information for all forecast horizons. Copyright © 2008 John Wiley & Sons, Ltd.     

The Forecasting Efficacy of Risk‐Neutral Moments for Crude Oil Volatility

This paper examines the information content of implied volatility for crude oil options as it relates to future realized volatility. Using data for the period 1996 to 2011 we find that implied volatility is an effective predictor of the month‐ahead realized volatility. We show that implied volatility subsumes the information content of contemporaneous volatility, and it contains incremental information on future volatility after controlling for contemporaneous volatility. Furthermore, incorporating risk‐neutral skewness, and especially kurtosis, improves the forecasting of realized volatility. Overall, the association between implied volatility and month‐ahead realized volatility is consistent with evidence documented for other asset classes, leading us to conclude that implied volatility serves as a reasonable proxy for expected volatility. Copyright © 2015 John Wiley & Sons, Ltd.     

The Role of High‐Frequency Intra‐daily Data,Daily Range and Implied Volatility in Multi‐period Value‐at‐Risk Forecasting

This paper assesses the informational content of alternative realized volatility estimators, daily range and implied volatility in multi‐period out‐of‐sample Value‐at‐Risk (VaR) predictions. We use the recently proposed Realized GARCH model combined with the skewed Student's t distribution for the innovations process and a Monte Carlo simulation approach in order to produce the multi‐period VaR estimates. Our empirical findings, based on the S&P 500 stock index, indicate that almost all realized and implied volatility measures can produce statistically and regulatory precise VaR forecasts across forecasting horizons, with the implied volatility being especially accurate in monthly VaR forecasts. The daily range produces inferior forecasting results in terms of regulatory accuracy and Basel II compliance. However, robust realized volatility measures, which are immune against microstructure noise bias or price jumps, generate superior VaR estimates in terms of capital efficiency, as they minimize the opportunity cost of capital and the Basel II regulatory capital. Copyright © 2013 John Wiley & Sons, Ltd.     

Does Information Help Intra‐Day Volatility Forecasts?

While much research related to forecasting return volatility does so in a univariate setting, this paper includes proxies for information flows to forecast intra‐day volatility for the IBEX 35 futures market. The belief is that volume or the number of transactions conveys important information about the market that may be useful in forecasting. Our results suggest that augmenting a variety of GARCH‐type models with these proxies lead to improved forecasts across a range of intra‐day frequencies. Furthermore, our results present an interesting picture whereby the PARCH model generally performs well at the highest frequencies and shorter forecasting horizons, whereas the component model performs well at lower frequencies and longer forecast horizons. Both models attempt to capture long memory; the PARCH model allows for exponential decay in the autocorrelation function, while the component model captures trend volatility, which dominates over a longer horizon. These characteristics are likely to explain the success of each model. Copyright © 2013 John Wiley & Sons, Ltd.     

Using CAViaR Models with Implied Volatility for Value‐at‐Risk Estimation

This paper proposes value‐at risk (VaR) estimation methods that are a synthesis of conditional autoregressive value at risk (CAViaR) time series models and implied volatility. The appeal of this proposal is that it merges information from the historical time series and the different information supplied by the market's expectation of risk. Forecast‐combining methods, with weights estimated using quantile regression, are considered. We also investigate plugging implied volatility into the CAViaR models—a procedure that has not been considered in the VaR area so far. Results for daily index returns indicate that the newly proposed methods are comparable or superior to individual methods, such as the standard CAViaR models and quantiles constructed from implied volatility and the empirical distribution of standardised residuals. We find that the implied volatility has more explanatory power as the focus moves further out into the left tail of the conditional distribution of S&P 500 daily returns. Copyright © 2012 John Wiley & Sons, Ltd.     

Can cointegration‐based forecasting outperform univariate models? An application to Asian exchange rates

Conventional wisdom holds that restrictions on low‐frequency dynamics among cointegrated variables should provide more accurate short‐ to medium‐term forecasts than univariate techniques that contain no such information; even though, on standard accuracy measures, the information may not improve long‐term forecasting. But inconclusive empirical evidence is complicated by confusion about an appropriate accuracy criterion and the role of integration and cointegration in forecasting accuracy. We evaluate the short‐ and medium‐term forecasting accuracy of univariate Box–Jenkins type ARIMA techniques that imply only integration against multivariate cointegration models that contain both integration and cointegration for a system of five cointegrated Asian exchange rate time series. We use a rolling‐window technique to make multiple out of sample forecasts from one to forty steps ahead. Relative forecasting accuracy for individual exchange rates appears to be sensitive to the behaviour of the exchange rate series and the forecast horizon length. Over short horizons, ARIMA model forecasts are more accurate for series with moving‐average terms of order >1. ECMs perform better over medium‐term time horizons for series with no moving average terms. The results suggest a need to distinguish between ‘sequential’ and ‘synchronous’ forecasting ability in such comparisons. Copyright © 2002 John Wiley & Sons, Ltd.     

Realized Volatility Forecasting of Agricultural Commodity Futures Using Long Memory and Regime Switching

We investigate the dynamic properties of the realized volatility of five agricultural commodity futures by employing the high‐frequency data from Chinese markets and find that the realized volatility exhibits both long memory and regime switching. To capture these properties simultaneously, we utilize a Markov switching autoregressive fractionally integrated moving average (MS‐ARFIMA) model to forecast the realized volatility by combining the long memory process with regime switching component, and compare its forecast performances with the competing models at various horizons. The full‐sample estimation results show that the dynamics of the realized volatility of agricultural commodity futures are characterized by two levels of long memory: one associated with the low‐volatility regime and the other with the high‐volatility regime, and the probability to stay in the low‐volatility regime is higher than that in the high‐volatility regime. The out‐of‐sample volatility forecast results show that the combination of long memory with switching regimes improves the performance of realized volatility forecast, and the proposed model represents a superior out‐of‐sample realized volatility forecast to the competing models. Copyright © 2016 John Wiley & Sons, Ltd.     

A Multiplicative Error Model with Heterogeneous Components for Forecasting Realized Volatility

To forecast realized volatility, this paper introduces a multiplicative error model that incorporates heterogeneous components: weekly and monthly realized volatility measures. While the model captures the long‐memory property, estimation simply proceeds using quasi‐maximum likelihood estimation. This paper investigates its forecasting ability using the realized kernels of 34 different assets provided by the Oxford‐Man Institute's Realized Library. The model outperforms benchmark models such as ARFIMA, HAR, Log‐HAR and HEAVY‐RM in within‐sample fitting and out‐of‐sample (1‐, 10‐ and 22‐step) forecasts. It performed best in both pointwise and cumulative comparisons of multi‐step‐ahead forecasts, regardless of loss function (QLIKE or MSE). Copyright © 2015 John Wiley & Sons, Ltd.     

Direction‐of‐change forecasting using a volatility‐based recurrent neural network

This paper investigates the profitability of a trading strategy, based on recurrent neural networks, that attempts to predict the direction‐of‐change of the market in the case of the NASDAQ composite index. The sample extends over the period 8 February 1971 to 7 April 1998, while the sub‐period 8 April 1998 to 5 February 2002 has been reserved for out‐of‐sample testing purposes. We demonstrate that the incorporation in the trading rule of estimates of the conditional volatility changes strongly enhances its profitability, after the inclusion of transaction costs, during bear market periods. This improvement is being measured with respect to a nested model that does not include the volatility variable as well as to a buy‐and‐hold strategy. We suggest that our findings can be justified by invoking either the ‘volatility feedback’ theory or the existence of portfolio insurance schemes in the equity markets. Our results are also consistent with the view that volatility dependence produces sign dependence. Copyright © 2008 John Wiley & Sons, Ltd.     

Modeling and forecasting realized volatility in German–Austrian continuous intraday electricity prices

This paper uses high‐frequency continuous intraday electricity price data from the EPEX market to estimate and forecast realized volatility. Three different jump tests are used to break down the variation into jump and continuous components using quadratic variation theory. Several heterogeneous autoregressive models are then estimated for the logarithmic and standard deviation transformations. Generalized autoregressive conditional heteroskedasticity (GARCH) structures are included in the error terms of the models when evidence of conditional heteroskedasticity is found. Model selection is based on various out‐of‐sample criteria. Results show that decomposition of realized volatility is important for forecasting and that the decision whether to include GARCH‐type innovations might depend on the transformation selected. Finally, results are sensitive to the jump test used in the case of the standard deviation transformation.     

Forecasting exchange rates using cointegration models and intra‐day data

We present a cointegration analysis on the triangle (USD–DEM, USD–JPY, DEM–JPY) of foreign exchange rates using intra‐day data. A vector autoregressive model is estimated and evaluated in terms of out‐of‐sample forecast accuracy measures. Its economic value is measured on the basis of trading strategies that account for transaction costs. We show that the typical seasonal volatility in high‐frequency data can be accounted for by transforming the underlying time scale. Results are presented for the original and the modified time scales. We find that utilizing the cointegration relation among the exchange rates and the time scale transformation improves forecasting results. Copyright © 2002 John Wiley & Sons, Ltd.     

An outlier robust GARCH model and forecasting volatility of exchange rate returns

Since volatility is perceived as an explicit measure of risk, financial economists have long been concerned with accurate measures and forecasts of future volatility and, undoubtedly, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model has been widely used for doing so. It appears, however, from some empirical studies that the GARCH model tends to provide poor volatility forecasts in the presence of additive outliers. To overcome the forecasting limitation, this paper proposes a robust GARCH model (RGARCH) using least absolute deviation estimation and introduces a valuable estimation method from a practical point of view. Extensive Monte Carlo experiments substantiate our conjectures. As the magnitude of the outliers increases, the one‐step‐ahead forecasting performance of the RGARCH model has a more significant improvement in two forecast evaluation criteria over both the standard GARCH and random walk models. Strong evidence in favour of the RGARCH model over other competitive models is based on empirical application. By using a sample of two daily exchange rate series, we find that the out‐of‐sample volatility forecasts of the RGARCH model are apparently superior to those of other competitive models. Copyright © 2002 John Wiley & Sons, Ltd.     

Evidence of long memory in short‐term interest rates

The issues of non‐stationarity and long memory of real interest rates are examined here. Autoregressive models allowing short‐term mean reversion are compared with fractional integration models in terms of their ability to explain the behaviour of the data and to forecast out‐of‐sample. The data used are weekly observations of 3‐month Eurodeposit rates for 10 countries, adjusted for inflation, for 14 years. Following Brenner, Harjes and Kroner, the volatility of these rates is shown to both exhibit GARCH effects and depend on the level of interest rates. Although relatively little support is found for the hypothesis of mean reversion, evidence of long memory in interest rate changes is found for seven countries. The out‐of‐sample forecasting performance for a year ahead of the fractional integrated models was significantly better than a no change. Copyright © 2003 John Wiley & Sons, Ltd.     

The Information Content of Intraday Implied Volatility for Volatility Forecasting

This study examines the intraday S&P 500 implied volatility index (VIX) to determine when the index contains the most information for volatility forecasting. The findings indicate that, in general, VIX levels around noon are most informative for predicting realized volatility. We posit that the VIX performs better during this time period because trading motivation around noon is less complex, and therefore trades contain more information on the market expectation of future volatility. Further investigation on the 2008 financial crisis period suggests that market participants become more cautious, and thus the forecasting performance is sustained until the market's close. Copyright © 2015 John Wiley & Sons, Ltd.     

Forecasting and trading currency volatility: an application of recurrent neural regression and model combination

In this paper, we examine the use of non‐parametric Neural Network Regression (NNR) and Recurrent Neural Network (RNN) regression models for forecasting and trading currency volatility, with an application to the GBP/USD and USD/JPY exchange rates. Both the results of the NNR and RNN models are benchmarked against the simpler GARCH alternative and implied volatility. Two simple model combinations are also analysed. The intuitively appealing idea of developing a nonlinear nonparametric approach to forecast FX volatility, identify mispriced options and subsequently develop a trading strategy based upon this process is implemented for the first time on a comprehensive basis. Using daily data from December 1993 through April 1999, we develop alternative FX volatility forecasting models. These models are then tested out‐of‐sample over the period April 1999–May 2000, not only in terms of forecasting accuracy, but also in terms of trading efficiency: in order to do so, we apply a realistic volatility trading strategy using FX option straddles once mispriced options have been identified. Allowing for transaction costs, most trading strategies retained produce positive returns. RNN models appear as the best single modelling approach yet, somewhat surprisingly, model combination which has the best overall performance in terms of forecasting accuracy, fails to improve the RNN‐based volatility trading results. Another conclusion from our results is that, for the period and currencies considered, the currency option market was inefficient and/or the pricing formulae applied by market participants were inadequate. Copyright © 2002 John Wiley & Sons, Ltd.     

Volatility Forecasting via MIDAS,HAR and their Combination: An Empirical Comparative Study for IBOVESPA

In this paper we compare several multi‐period volatility forecasting models, specifically from MIDAS and HAR families. We perform our comparisons in terms of out‐of‐sample volatility forecasting accuracy. We also consider combinations of the models' forecasts. Using intra‐daily returns of the BOVESPA index, we calculate volatility measures such as realized variance, realized power variation and realized bipower variation to be used as regressors in both models. Further, we use a nonparametric procedure for separately measuring the continuous sample path variation and the discontinuous jump part of the quadratic variation process. Thus MIDAS and HAR specifications with the continuous sample path and jump variability measures as separate regressors are estimated. Our results in terms of mean squared error suggest that regressors involving volatility measures which are robust to jumps (i.e. realized bipower variation and realized power variation) are better at forecasting future volatility. However, we find that, in general, the forecasts based on these regressors are not statistically different from those based on realized variance (the benchmark regressor). Moreover, we find that, in general, the relative forecasting performances of the three approaches (i.e. MIDAS, HAR and forecast combinations) are statistically equivalent. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting volatility with support vector machine‐based GARCH model

Recently, support vector machine (SVM), a novel artificial neural network (ANN), has been successfully used for financial forecasting. This paper deals with the application of SVM in volatility forecasting under the GARCH framework, the performance of which is compared with simple moving average, standard GARCH, nonlinear EGARCH and traditional ANN‐GARCH models by using two evaluation measures and robust Diebold–Mariano tests. The real data used in this study are daily GBP exchange rates and NYSE composite index. Empirical results from both simulation and real data reveal that, under a recursive forecasting scheme, SVM‐GARCH models significantly outperform the competing models in most situations of one‐period‐ahead volatility forecasting, which confirms the theoretical advantage of SVM. The standard GARCH model also performs well in the case of normality and large sample size, while EGARCH model is good at forecasting volatility under the high skewed distribution. The sensitivity analysis to choose SVM parameters and cross‐validation to determine the stopping point of the recurrent SVM procedure are also examined in this study. Copyright © 2009 John Wiley & Sons, Ltd.     

Are industry‐level indicators more helpful to forecast industrial stock volatility? Evidence from Chinese manufacturing purchasing managers index

Effectively explaining and accurately forecasting industrial stock volatility can provide crucial references to develop investment strategies, prevent market risk and maintain the smooth running of national economy. This paper aims to discuss the roles of industry‐level indicators in industrial stock volatility. Selecting Chinese manufacturing purchasing managers index (PMI) and its five component PMI as the proxies of industry‐level indicators, we analyze the contributions of PMI on industrial stock volatility and further compare the volatility forecasting performances of PMI, macroeconomic fundamentals and economic policy uncertainty (EPU), by constructing the individual and combination GARCH‐MIDAS models. The empirical results manifest that, first, most of the PMI has significant negative effects on industrial stock volatility. Second, PMI which focuses on the industrial sector itself is more helpful to forecast industrial stock volatility compared with the commonly used macroeconomic fundamentals and economic policy uncertainty. Finally, the combination GARCH‐MIDAS approaches based on DMA technique demonstrate more excellent predictive abilities than the individual GARCH‐MIDAS models. Our major conclusions are robust through various robustness checks.