Forecasting the volatility of S&P depositary receipts using GARCH-type models under intraday range-based and return-based proxy measures

We employ four various GARCH-type models, incorporating the skewed generalized t (SGT) errors into those returns innovations exhibiting fat-tails, leptokurtosis and skewness to forecast both volatility and value-at-risk (VaR) for Standard & Poor's Depositary Receipts (SPDRs) from 2002 to 2008. Empirical results indicate that the asymmetric EGARCH model is the most preferable according to purely statistical loss functions. However, the mean mixed error criterion suggests that the EGARCH model facilitates option buyers for improving their trading position performance, while option sellers tend to favor the IGARCH/EGARCH model at shorter/longer trading horizon. For VaR calculations, although these GARCH-type models are likely to over-predict SPDRs' volatility, they are, nevertheless, capable of providing adequate VaR forecasts. Thus, a GARCH genre of model with SGT errors remains a useful technique for measuring and managing potential losses on SPDRs under a turbulent market scenario.     

Pricing and hedging options with GARCH-stable proxy volatilities

This article considers modelling nonnormality in return with stable Paretian (SP) innovations in generalized autoregressive conditional heteroskedasticity (GARCH), exponential generalized autoregressive conditional heteroskedasticity (EGARCH) and Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH) volatility dynamics. The forecasted volatilities from these dynamics have been used as a proxy to the volatility parameter of the Black–Scholes (BS) model. The performance of these proxy-BS models has been compared with the performance of the BS model of constant volatility. Using a cross section of S&P500 options data, we find that EGARCH volatility forecast with SP innovations is an excellent proxy to BS constant volatility in terms of pricing. We find improved performance of hedging for an illustrative option portfolio. We also find better performance of spectral risk measure (SRM) than value-at-risk (VaR) and expected shortfall (ES) in estimating option portfolio risk in case of the proxy-BS models under SP innovations.

Abbreviation: generalized autoregressive conditional heteroskedasticity (GARCH), exponential generalized autoregressive conditional heteroskedasticity (EGARCH) and Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH)     

Calculating Value-at-Risk for high-dimensional time series using a nonlinear random mapping model

In this study, we propose a non-linear random mapping model called GELM. The proposed model is based on a combination of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and the Extreme Learning Machine (ELM), and can be used to calculate Value-at-Risk (VaR). Alternatively, the GELM model is a non-parametric GARCH-type model. Compared with conventional models, such as the GARCH models, ELM, and Support Vector Machine (SVM), the computational results confirm that the GELM model performs better in volatility forecasting and VaR calculation in terms of efficiency and accuracy. Thus, the GELM model can be an essential tool for risk management and stress testing.     

Asymmetry, realised volatility and stock return risk estimates

In this paper we estimate minimum capital risk requirements for short and long positions with three investment horizons, using the traditional GARCH model and two other GARCH-type models that incorporate the possibility of asymmetric responses of volatility to price changes. We also address the problem of the extremely high estimated persistence of the GARCH model to generate observed volatility patterns by including realised volatility as an explanatory variable into the model??s variance equation. The results suggest that the inclusion of realised volatility improves the GARCH forecastability as well as its ability to calculate accurate minimum capital risk requirements and makes it quite competitive when compared with asymmetric conditional heteroscedastic models such as the GJR and the EGARCH.     

Pricing Nikkei 225 Options Using Realized Volatility

This article examines option pricing performance using realized volatilities with or without handling microstructure noise, non‐trading hours and large jumps. The dynamics of realized volatility is specified by ARFIMA(X) and HAR(X) models. The main results using put options on the Nikkei 225 index are that: (i) the ARFIMAX model performs best; (ii) the Hansen and Lunde (2005a) adjustment for non‐trading hours improves the performance; (iii) methods for reducing microstructure noise‐induced bias yield better performance, while if the Hansen–Lunde adjustment is used, the other methods are not necessarily needed; and (iv) the performance is unaffected by removing large jumps from realized volatility.     

A new approach to bad news effects on volatility: the multiple-sign-volume sensitive regime EGARCH model (MSV-EGARCH)

In this paper, using daily data for six major international stock market indexes and a modified EGARCH specification, the links between stock market returns, volatility and trading volume are investigated in a new nonlinear conditional variance framework with multiple regimes and volume effects. Volatility forecast comparisons, using the Harvey-Newbold test for multiple forecasts encompassing, seem to demonstrate that the MSV-EGARCH complex threshold structure is able to correctly fit GARCH-type dynamics of the series under study and dominates competing standard asymmetric models in several of the considered stock indexes.

Long-Memory,Asymmetry and Fat-Tailed GARCH Models in Value-at-Risk Estimation: Empirical Evidence from the Global Real Estate Markets

In this paper, we address the question of whether long memory, asymmetry, and fat-tails in global real estate markets volatility matter when forecasting the two most popular measures of risk in financial markets, namely Value-at-risk (VaR) and Expected Shortfall (ESF), for both short and long trading positions. The computations of both VaR and ESF are conducted with three long memory GARCH-class models including the Fractionally Integrated GARCH (FIGARCH), Hyperbolic GARCH (HYGARCH), and Fractionally Integrated Asymmetric Power ARCH (FIAPARCH). These models are estimated under three alternative innovation’s distributions: normal, Student, and skewed Student. To test the efficacy of the forecast, we employ various backtesting methodologies. Our empirical findings show that considering for long memory, fat-tails, and asymmetry performs better in predicting a one-day-ahead VaR and ESF for both short and long trading positions. In particular, the forecasting ability analysis points out that the FIAPARCH model under skewed Student distribution turns out to improve substantially the VaR and ESF forecasts. These results may have several potential implications for the market participants, financial institutions, and the government.

     

Volatility and Market Risk of Rubber Price in Malaysia: Pre- and Post-Global Financial Crisis

The volatility in rubber price is a significant risk to producers, traders, consumers and others who are involved in the production and marketing of natural rubber. Such being the case, forecasting the rubber price volatility is desired to assist in decision-making in this uncertain situation. The 2008 Global Financial Crisis caused some disruptions and uncertainties in the future supply or demand for natural rubber and thus leading to higher rubber price volatility. Using ARCH-type models, this paper intends to model the dynamics of the price volatility of Standard Malaysia Rubber Grade 20 (SMR 20) in the Malaysian market before and after the Global Financial Crisis. Additionally, Value-at-Risk (VaR) approach is implemented to evaluate the market risk of SMR 20. Our empirical result denotes the existence of volatility clustering and long memory volatility in the SMR 20 market for both crisis periods. Leverage effect is also detected in the SMR 20 market where negative innovations (bad news) have a larger impact on the volatility than positive innovations (good news) for post-crisis period. When tested with Superior Predictive Ability (SPA) test, FIGARCH model is the best model across five loss functions for short- and long-term forecasts for pre-crisis period. Meanwhile, over post-crisis period, FIGARCH and GJR GARCH indicate the superior out-of-sample-forecast results and better forecasting accuracy over short- and long-term horizons, respectively. In terms of market risk, the short trading position encounters higher risk or greater losses than the long trading position at both 1 and 5 % VaR quantile for pre-crisis period. In contrast, over post-crisis period, long traders of rubber SMR 20 tend to face limited gains but unlimited losses.

     

Conditional volatility and correlations of weekly returns and the VaR analysis of 2008 stock market crash

Modelling of conditional volatilities and correlations across asset returns is an integral part of portfolio decision making and risk management. Over the past three decades there has been a trend towards increased asset return correlations across markets, a trend which has been accentuated during the recent financial crisis. We shall examine the nature of asset return correlations using weekly returns on futures markets and investigate the extent to which multivariate volatility models proposed in the literature can be used to formally characterize and quantify market risk. In particular, we ask how adequate these models are for modelling market risk at times of financial crisis. In doing so we consider a multivariate t version of the Gaussian dynamic conditional correlation (DCC) model proposed by Engle (2002), and show that the t-DCC model passes the usual diagnostic tests based on probability integral transforms, but fails the value at risk (VaR) based diagnostics when applied to the post 2007 period that includes the recent financial crisis.     

Can GARCH-class models capture long memory in WTI crude oil markets?

This paper investigates the issue whether GARCH-type models can well capture the long memory widely existed in the volatility of WTI crude oil returns. In this frame, we model the volatility of spot and futures returns employing several GARCH-class models. Then, using two non-parametric methods, detrended fluctuation analysis (DFA) and rescaled range analysis (R/S), we compare the long memory properties of conditional volatility series obtained from GARCH-class models to that of actual volatility series. Our results show that GARCH-class models can well capture the long memory properties for the time scale larger than a year. However, for the time scale smaller than a year, the GARCH-class models are misspecified.     

Power monotonicity in detecting volatility levels change

We show that the CUSUM and LM tests for structural change in the volatility process enjoy monotonic power. The framework is general including many recently proposed non-stationary GARCH-type models. The result is in contrast to the well-known issue of non-monotonic power for the CUSUM-based tests for changing mean. Simulations and an empirical example provide further support.     

Prediction of volatility based on realized-GARCH-kernel-type models: Evidence from China and the U.S.

We propose three Realized-GARCH-Kernel-type models which do not make the distribution assumptions on the return disturbance terms. We use this type of model to predict the return volatilities of the 50ETF in China and the S&P500 index in the U.S. The semiparametric kernel density estimator of our models, which captures the skewness, asymmetry and fat-tail of financial assets, performs well both statistically and economically. Our models have more predictive power than other eight comparable volatility models that need to pre-specify the distribution of the disturbance terms. Our results are robust to eight measures of realized volatility. Using option straddle strategies, we show that our models generate larger trading profits and greater Sharpe ratios than the other competing models.     

Estimating value-at-risk under a Heath–Jarrow–Morton framework with jump

This article proposes a new methodology for measuring Value-at-Risk (hereafter VaR) using a model that incorporates both volatility and jumps. Heath–Jarrow–Morton (HJM) model has been used for the valuation of interest rate derivatives. This study extends the use of HJM model to the estimation VaR. This article specifically uses a two-factor HJM jump-diffusion model for the computation. The study models the Eurodollar futures prices using its derivatives. In addition, this article uses a new volatility specification of Ze-To (2002) to construct the HJM dynamics. The result indicates that the VaR model using HJM jump-diffusion framework performs well in capturing the nonnormality and in providing accurate VaR forecasts in the in-sample and out-sample tests.     

Forecasting volatility in the Chinese stock market under model uncertainty

Volatility forecasting is an important issue in empirical finance. In this paper, the main purpose is to apply the model averaging techniques to reduce volatility model uncertainty and improve volatility forecasting. Six GARCH-type models are considered as candidate models for model averaging. As to the Chinese stock market, the largest emerging market in the world, the empirical study shows that forecast combination using model averaging can be a better approach than the individual forecasts.     

Does measurement error matter in volatility forecasting? Empirical evidence from the Chinese stock market

Based on methods developed by Bollerslev et al. (2016), we explicitly accounted for the heteroskedasticity in the measurement errors and for the high volatility of Chinese stock prices; we proposed a new model, the LogHARQ model, as a way to appropriately forecast the realized volatility of the Chinese stock market. Out-of-sample findings suggest that the LogHARQ model performs better than existing logarithmic and linear forecast models, particularly when the realized quarticity is large. The better performance is also confirmed by the utility based economic value test through volatility timing.     

Score-driven Markov-switching EGARCH models: an application to systematic risk analysis

We introduce new Markov-switching (MS) dynamic conditional score (DCS) exponential generalized autoregressive conditional heteroscedasticity (EGARCH) models, to be used by practitioners for forecasting value-at-risk (VaR) and expected shortfall (ES) in systematic risk analysis. We use daily log-return data from the Standard & Poor’s 500 (S&P 500) index for the period 1950–2016. The analysis of the S&P 500 is useful, for example, for investors of (i) well-diversified US equity portfolios; (ii) S&P 500 futures and options traded at Chicago Mercantile Exchange Globex; (iii) exchange traded funds (ETFs) related to the S&P 500. The new MS DCS-EGARCH models are alternatives to of the recent MS Beta-t-EGARCH model that uses the symmetric Student’s t distribution for the error term. For the new models, we use more flexible asymmetric probability distributions for the error term: Skew-Gen-t (skewed generalized t), EGB2 (exponential generalized beta of the second kind) and NIG (normal-inverse Gaussian) distributions. For all MS DCS-EGARCH models, we identify high- and low-volatility periods for the S&P 500. We find that the statistical performance of the new MS DCS-EGARCH models is superior to that of the MS Beta-t-EGARCH model. As a practical application, we perform systematic risk analysis by forecasting VaR and ES.

Abbreviation Single regime (SR); Markov-switching (MS); dynamic conditional score (DCS); exponential generalized autoregressive conditional heteroscedasticity (EGARCH); value-at-risk (VaR); expected shortfall (ES); Standard & Poor's 500 (S&P 500); exchange traded funds (ETFs); Skew-Gen-t (skewed generalized t); EGB2 (exponential generalized beta of the second kind); NIG (normal-inverse Gaussian); log-likelihood (LL); standard deviation (SD); partial autocorrelation function (PACF); likelihood-ratio (LR); ordinary least squares (OLS); heteroscedasticity and autocorrelation consistent (HAC); Akaike information criterion (AIC); Bayesian information criterion (BIC); Hannan-Quinn criterion (HQC).     

Translating financial integration into correlation risk: A weekly reporting's viewpoint for the volatility behavior of stock markets

We apply the multivariate extension of GARCH-type models in order to assess the systematic and systemic risks as well as the joint volatility behaviors of the U.S. and three European financial markets (Andersen et al., 2010). Therefore, we can appraise the co-movements of the four previous financial markets as well as the joint behavior of their respective volatilities (i.e. systemic risk). Moreover, the resulting conditional variance and covariance metrics allow for handling volatility spillovers (i.e. contagion risk in terms of transmitting volatility shocks from one market place to another market place). Indeed, results highlight the unprecedented high systemic risk levels (i.e. joint increased volatility levels) as well as a high contagion risk (i.e. volatility spillover) during the subprime mortgage market crisis. The transmission process of volatility shocks reveals to be simultaneous across financial markets due to a strong arbitrage activity and electronic trading practices among others. Most importantly, the estimated conditional correlations exhibit an upward sloping trend, which underlines an increase in the correlation risk between financial markets in the late nineties or early 2000. Thus, our major findings are twofold. First, we characterize the dynamic correlation risk across financial markets. Second, we also confirm the increasing and nonlinear trend in the correlation risk, which we are able to quantify.     

Realized volatility models and alternative Value-at-Risk prediction strategies

We assess the Value-at-Risk (VaR) forecasting performance of recently proposed realized volatility (RV) models combined with alternative parametric and semi-parametric quantile estimation methods. A benchmark inter-daily GJR-GARCH model is also employed. Based on four asset classes, i.e. equity, FOREX, fixed income and commodity, and a turbulent six year out-of-sample period (2007–2013), we find that statistical accuracy and regulatory compliance is essentially improved when we use quantile methods which account for the fat tails and the asymmetry of the innovations distribution. In particular, empirical analysis gives evidence in favor of the skewed student distribution and the Extreme Value Theory (EVT) method. Nonetheless, efficiency of VaR estimates, as defined by the minimization of Basel II capital requirements and its opportunity costs, is reassured only with the use of realized volatility models. Overall, empirical evidence support the use of an asymmetric HAR realized volatility model coupled with the EVT method since it produces statistically accurate VaR forecasts which comply with Basel II accuracy mandates and allows for more efficient capital allocations.     

Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

We compare the backtesting performance of ARMA-GARCH models with the most common types of infinitely divisible innovations, fit with both full maximum likelihood estimation (MLE) and quasi maximum likelihood estimation (QMLE). The innovation types considered are the Gaussian, Student’s t, α-stable, classical tempered stable (CTS), normal tempered stable (NTS) and generalized hyperbolic (GH) distributions. In calm periods of decreasing volatility, MLE and QMLE produce near identical performance in forecasting value-at-risk (VaR) and conditional value-at-risk (CVaR). In more volatile periods, QMLE can actually produce superior performance for CTS, NTS and α-stable innovations. While the t-ARMA-GARCH model has the fewest number of VaR violations, rejections by the Kupeic and Berkowitz tests suggest excessively large forecasted losses. The α-stable, CTS and NTS innovations compare favourably, with the latter two also allowing for option pricing under a single market model.