Volatility Forecasting Models Research Articles

Good risk measures, bad statistical assumptions, ugly risk forecasts

AbstractThis paper proposes the time‐heterogeneous Student's t autoregressive model as an alternative to the various volatility forecast models documented in the literature. The empirical results indicate that: (i) the proposed model has better forecasting performance than other commonly used models, and (ii) the problem of reliable risk measurement arises primarily from the model risk associated with risk forecast models rather than the particular risk measure for computing risk. Based on the results, the paper makes recommendations to regulators and practitioners.

Volatility forecasting with Hybrid‐long short‐term memory models: Evidence from the COVID‐19 period

AbstractVolatility forecasting, a central issue in financial risk modelling and management, has attracted increasing attention after several major financial market crises. In this article, we draw upon the literature on volatility forecasting and hybrid models to construct the Hybrid‐long short‐term memory (LSTM) models to forecast the intraday realized volatility in three major US stock indexes. We construct the hybrid models by combining one or multiple traditional time series models with the LSTM model, and incorporating either the estimated parameters, or the predicted volatility, or both from the statistical models as additional input values into the LSTM model. We perform the out‐of‐sample test of our Hybrid‐LSTM models in volatility forecasting during the coronavirus disease 2019 (COVID‐19) period. Empirical results show that the Hybrid‐LSTM models can still significantly improve the volatility forecasting performance of the LSTM model during the COVID‐19 period. By analysing how the construction methods may influence the forecasting performance of the Hybrid‐LSTM models, we provide some suggestions on their design. Finally, we identify the optimal Hybrid‐LSTM model for each stock index and compare its performance with the LSTM model on each day during our sample period. We find that the Hybrid‐LSTM models' great capability of capturing market dynamics explains their good performance in forecasting.

A generalized heterogeneous autoregressive model using market information

This paper introduces a novel class of volatility forecasting models that incorporate market realized (co)variances and semi(co)variances within the framework of a heterogeneous autoregressive (HAR) model. Our empirical analysis shows statistically and economically significant forecasting gains. For our most parsimonious market-HAR specification, stock volatility forecasting is improved by 9.80% points. Using a mixed sampling frequency market-HAR variant with low (high) sampling frequency for the stock (market) improves forecasting by a further 6.90% points. Our paper also develops noise-robust estimators to facilitate the use of realized semi(co)variances at high sampling frequencies.

Forecasting green bond volatility via novel heterogeneous ensemble approaches

Green bonds are powerful tools for fighting against climate change and typically exhibit more volatility than conventional bonds do. However, the volatility forecasting of green bond has received little attention in previous literature. This study proposes two novel heterogeneous ensemble models, which differ from common volatility forecasting in that they are combine advanced tree-based ensemble models and exogenous predictors from other financial and commodity markets to forecast the volatility of green bonds. Validated on multiple green bonds indexes, loss functions, and time horizons, the comparative results show that the incorporation of exogenous predictors can enhance the predictive accuracy of volatility forecasting models, which is also confirmed by the marginal effects illustrated by SHapley Additive exPlanations (SHAP) values. The proposed EX-SEL model significantly outperforms the benchmark models in most cases. The results of the robustness check further indicate that the empirical results are robust to alternative volatility estimators, extreme events such as the COVID-19 pandemic, and alternative selection strategies.

How to Promote the Performance of Parametric Volatility Forecasts in the Stock Market? A Neural Networks Approach.

This study uses the fourteen stock indices as the sample and then utilizes eight parametric volatility forecasting models and eight composed volatility forecasting models to explore whether the neural network approach and the settings of leverage effect and non-normal return distribution can promote the performance of volatility forecasting, and which one of the sixteen models possesses the best volatility forecasting performance. The eight parametric volatility forecasts models are composed of the generalized autoregressive conditional heteroskedasticity (GARCH) or GJR-GARCH volatility specification combining with the normal, Student’s t, skewed Student’s t, and generalized skewed Student’s t distributions. Empirical results show that, the performance for the composed volatility forecasting approach is significantly superior to that for the parametric volatility forecasting approach. Furthermore, the GJR-GARCH volatility specification has better performance than the GARCH one. In addition, the non-normal distribution does not have better forecasting performance than the normal distribution. In addition, the GJR-GARCH model combined with both the normal distribution and a neural network approach has the best performance of volatility forecasting among sixteen models. Thus, a neural network approach significantly promotes the performance of volatility forecasting. On the other hand, the setting of leverage effect can encourage the performance of volatility forecasting whereas the setting of non-normal distribution cannot.

Multi-Transformer: A New Neural Network-Based Architecture for Forecasting S&P Volatility

Events such as the Financial Crisis of 2007–2008 or the COVID-19 pandemic caused significant losses to banks and insurance entities. They also demonstrated the importance of using accurate equity risk models and having a risk management function able to implement effective hedging strategies. Stock volatility forecasts play a key role in the estimation of equity risk and, thus, in the management actions carried out by financial institutions. Therefore, this paper has the aim of proposing more accurate stock volatility models based on novel machine and deep learning techniques. This paper introduces a neural network-based architecture, called Multi-Transformer. Multi-Transformer is a variant of Transformer models, which have already been successfully applied in the field of natural language processing. Indeed, this paper also adapts traditional Transformer layers in order to be used in volatility forecasting models. The empirical results obtained in this paper suggest that the hybrid models based on Multi-Transformer and Transformer layers are more accurate and, hence, they lead to more appropriate risk measures than other autoregressive algorithms or hybrid models based on feed forward layers or long short term memory cells.

Forecasting the Volatility of the Cryptocurrency Market by GARCH and Stochastic Volatility

This study examines the volatility of nine leading cryptocurrencies by market capitalization—Bitcoin, XRP, Ethereum, Bitcoin Cash, Stellar, Litecoin, TRON, Cardano, and IOTA-by using a Bayesian Stochastic Volatility (SV) model and several GARCH models. We find that when we deal with extremely volatile financial data, such as cryptocurrencies, the SV model performs better than the GARCH family models. Moreover, the forecasting errors of the SV model, compared with the GARCH models, tend to be more accurate as forecast time horizons are longer. This deepens our insight into volatility forecast models in the complex market of cryptocurrencies.

Complexity of exchange rate movement, analysis and volatility forecasting models: a review

For obvious development in literature, various researchers and experts have relied on their area of expertise in the field of financial econometric to prove a substantive performance of one model o...

Complexity of exchange rate movement, analysis and volatility forecasting models: a review

Complexity of exchange rate movement, analysis and volatility forecasting models: a review

Further Study of the DEA-Based Framework for Performance Evaluation of Competing Crude Oil Prices’ Volatility Forecasting Models

The super-efficiency data envelopment analysis model is innovative in evaluating the performance of crude oil prices’ volatility forecasting models. This multidimensional ranking, which takes account of multiple criteria, gives rise to a unified decision as to which model performs best. However, the rankings are unreliable because some efficiency scores are infeasible solutions in nature. What’s more, the desirability of indexes is worth discussing so as to avoid incorrect rankings. Hence, herein we introduce four models, which address the issue of undesirable characteristics of indexes and infeasibility of the super efficiency models. The empirical results reveal that the new rankings are more robust and quite different from the existing results.

Modeling conditional volatility by incorporating non-regular trading hours into the APARCH model

ABSTRACT This study aims to evaluate how the after-market and pre-opening periods affect the estimation of conditional volatility one day ahead. Volatility features quite a lot in Finance studies because it is a fundamental parameter in derivatives pricing, the efficient allocation of portfolios, and risk management. The results are relevant for investment agents to be able to refine volatility forecasting models and achieve better results in derivatives pricing, risk management, and portfolio optimization. We used the asymmetric power autoregressive conditional heteroscedasticity (APARCH) model, incorporating the after-market, pre-opening, and total overnight periods to assess whether they contain important information for modeling volatility. We analyzed the 20 stocks of Brazilian companies listed on the São Paulo Stock, Commodities, and Futures Exchange (BM&FBovespa) and also belonging to the BR Titans 20 with ADRs listed on the New York Stock Exchange and the Nasdaq. The results were evaluated in-sample using the corrected Akaike information criterion (AICc) and the statistical significance of the coefficients, and out-of-sample using root mean squared error (RMSE), mean absolut percentage error (MAPE), the R² of the Mincer-Zarnowitz regression, and the Diebold Mariano test. The analysis does not enable it to be claimed which is the best model, because there is no unanimity among all the stocks; however, non-regular trading hours were shown to incorporate important information for most of the stocks. Furthermore, the models that incorporated the pre-opening period generally obtained superior results to the models that incorporated the after-market period, demonstrating that this period contains important information for forecasting conditional volatility.

Symmetric volatility forecast models for crude oil price in Nigeria

Symmetric volatility forecast models for crude oil price in Nigeria

Time-varying Variance Scaling: Application of the Fractionally Integrated ARMA Model

Time-varying variance scaling is the technique by which a mean-variance investor can volatility manage a portfolio by adjusting allocation according to the attractiveness of the mean-variance trade-off, μt/σt2. This study shows that the choice of volatility forecasting models significantly affects performance. We find that the fractionally integrated ARMA model provides significantly better scaling input than the simple historical average volatility for most test portfolios examined by this study. For standard momentum portfolios, however, using the simple historical average as input for volatility scaling resulted in the best performance in many cases.

Cross-border exchanges and volatility forecasting

We test for the performance of a series of volatility forecasting models (GARCH 1,1; EGARCH 1,1; CGARCH) in the context of several indices from the two oldest cross-border exchanges (Euronext; OMX). Our findings overall indicate that the EGARCH (1,1) model outperforms the other two, both before and after the outbreak of the global financial crisis. Controlling for the presence of feedback traders, the accuracy of the EGARCH (1,1) model is not affected, something further confirmed for both the pre and post crisis periods. Overall, ARCH effects can be found in the Euronext and OMX indices, with our results further indicating the presence of significant positive feedback trading in several of our tests.

PREDICTIVE ACCURACY OF FUTURES OPTIONS IMPLIED VOLATILITY: THE CASE OF THE EXCHANGE RATE FUTURES MEXICAN PESO-US DOLLAR

There has been substantial research effort aimed to forecast futures price return volatilities of financial assets. A significant part of the literature shows that volatility forecast accuracy is not easy to estimate regardless of the forecasting model applied. This paper examines the volatility accuracy of several volatility forecast models for the case of the Mexican peso-USD exchange rate futures returns. The models applied here are a univariate GARCH, a multivariate ARCH (the BEKK model), two option implied volatility models and a composite forecast model. The composite model includes time-series (historical) and option implied volatility forecasts. Different to other works in the literature, in this paper there is a more rigorous analysis of the option implied volatilities calculations. The results show that the option implied models are superior to the historical models in terms of accuracy and that the composite forecast model was the most accurate one (compared to the alternative models) having the lowest mean-squared-errors. However, the results should be taken with caution given that the coefficient of determination in the regressions was relatively low. According to these findings it is recommended to use a composite forecast model if both types of data are available i.e. the time-series (historical) and the option implied.

Comparative Study of Volatility Forecasting Models: The Case of Malaysia, Indonesia, Hong Kong and Japan Stock Markets

This paper aims to investigate the effectiveness of four volatility forecasting models, i.e. Exponential Weighted Moving Average (EWMA), Autoregressive Integrated Moving Average (ARIMA) and Generalized Auto-Regressive Conditional Heteroscedastic (GARCH), in four stock markets Indonesia, Malaysia, Japan and Hong Kong. Using monthly closing stock index prices collected from 1st January 1998 to 31st December 2015 for the four selected countries, results obtained confirm that volatility in developed markets is not necessarily always lower than the volatility in emerging markets. Among all the three models, GARCH (1, 1) model is found to be the best forecasting model for stock markets in Malaysia, Indonesia, and Japan, while EWMA model is found to be the best forecasting model for Hong Kong stock market. The outperformance of GARCH (1, 1) found supports again what is found in Minkah (2007).

Modelling persistence in conditional volatility of asset returns

Studies on volatility forecasting models indicate superior performance of generalised autoregressive conditional heteroscedasticity (GARCH) type models in the modelling conditional variance of asset returns. The utility of GARCH parameters lies in their ability in explaining the persistence of the conditional variance. The estimate of persistence provides a quantitative measure of the impact of a sudden significant change in the asset return on its future volatility. This study attempts to analyse the magnitude and time-evolving pattern in the persistence of conditional volatility using data on S&P CNX NIFTY 50 (henceforth, Nifty) benchmark index. The GARCH (1, 1) model is fitted on daily returns and a simple iterative scheme is used to re-estimate GARCH parameters on samples of different sizes and different time periods. The GARCH estimates obtained through repeated estimations furnish empirical evidence on the nature and consistency of the persistence parameter. Findings of the study confirm high persistence in the volatility process and indicate a positive relationship between the conditional volatility and volatility persistence.

Modelling persistence in conditional volatility of asset returns

Studies on volatility forecasting models indicate superior performance of generalised autoregressive conditional heteroscedasticity (GARCH) type models in the modelling conditional variance of asset returns. The utility of GARCH parameters lies in their ability in explaining the persistence of the conditional variance. The estimate of persistence provides a quantitative measure of the impact of a sudden significant change in the asset return on its future volatility. This study attempts to analyse the magnitude and time-evolving pattern in the persistence of conditional volatility using data on S&P CNX NIFTY 50 (henceforth, Nifty) benchmark index. The GARCH (1, 1) model is fitted on daily returns and a simple iterative scheme is used to re-estimate GARCH parameters on samples of different sizes and different time periods. The GARCH estimates obtained through repeated estimations furnish empirical evidence on the nature and consistency of the persistence parameter. Findings of the study confirm high persistence in the volatility process and indicate a positive relationship between the conditional volatility and volatility persistence.

Forecasting Stock Market Volatility: The Gains from Using Intraday Data

There is evidence that volatility forecasting models that use intraday data produce superior forecast accuracy as compared with that delivered by the models that use daily data. However, this evidence is still sparse and incomplete in the stock markets. This paper extends previous studies on forecasting stock market volatility in several important directions and comprehensively assesses the gains in forecast accuracy provided by intraday data. First, we use an extensive set of intraday data on 28 single stocks and 23 stock market indices. Second, in our study we use forecast horizons ranging from 1 day to 6 months. Third, we compare forecasting abilities of several competing models. We find that the amount of gains depends on the length of the forecast horizon, on the forecasting model, and on whether the volatility is forecasted for a single stock or a stock market index. The major finding of our empirical study is that intraday data allow one to increase the forecast accuracy by 10% to 30%. Thus, the gains from using intraday data are rather significant. Surprisingly, we find that the gains in predictive accuracy from intraday data persist over longer forecast horizons and are greater for stock market indices than for single stocks.

Calculation of solar irradiation prediction intervals combining volatility and kernel density estimates

In order to integrate solar energy into the grid it is important to predict the solar radiation accurately, where forecast errors can lead to significant costs. Recently, the increasing statistical approaches that cope with this problem is yielding a prolific literature. In general terms, the main research discussion is centred on selecting the “best” forecasting technique in accuracy terms. However, the need of the users of such forecasts require, apart from point forecasts, information about the variability of such forecast to compute prediction intervals. In this work, we will analyze kernel density estimation approaches, volatility forecasting models and combination of both of them in order to improve the prediction intervals performance. The results show that an optimal combination in terms of prediction interval statistical tests can achieve the desired confidence level with a lower average interval width. Data from a facility located in Spain are used to illustrate our methodology.