Forecasting the S&P 500 index volatility

This study introduces a new pre-differencing transformation for the AR1MA model for forecasting S&P 500 index volatility. The out of sample forecasting performance of the ARIMA model using the new pre-differencing transformation is compared with the out of sample forecasting performance of the mean reversion model and the GARCH model. The ARIMA model using the new pre-differencing transformation introduced in this study is found to be superior to both the mean reversion model and the GARCH model in forecasting monthly S&P 500 index volatility for the forecast comparison periods used in this study.     

Realized volatility transmission: The role of jumps and leverage effects

This paper is the first to employ a multivariate extension of the LHAR–CJ model for realized volatility of Corsi and Renó (2012) considering continuous and jump volatility components and leverage effects. The model is applied to financial (S&P 500), commodity (WTI crude oil) and forex (US$/EUR) intraday futures data and allows new insights in the transmission mechanisms among these markets. Besides significant leverage effects, we find that the jump components of all considered assets do not contain incremental information for the one-step ahead realized volatility. The volatility of S&P 500 and US$/EUR exchange rate futures exhibits significant spillovers to the realized volatility of WTI. Moreover, decreasing equity prices appear to increase volatility in other markets, while strengthening of the US$ seems to calm down the crude oil market.     

Correlations and volatility spillovers across commodity and stock markets: Linking energies,food, and gold

This paper employs a VAR-GARCH model to investigate the return links and volatility transmission between the S&P 500 and commodity price indices for energy, food, gold and beverages over the turbulent period from 2000 to 2011. Understanding the price behavior of commodity prices and the volatility transmission mechanism between these markets and the stock exchanges are crucial for each participant, including governments, traders, portfolio managers, consumers, and producers. For return and volatility spillover, the results show significant transmission among the S&P 500 and commodity markets. The past shocks and volatility of the S&P 500 strongly influenced the oil and gold markets. This study finds that the highest conditional correlations are between the S&P 500 and gold index and the S&P 500 and WTI index. We also analyze the optimal weights and hedge ratios for commodities/S&P 500 portfolio holdings using the estimates for each index. Overall, our findings illustrate several important implications for portfolio hedgers for making optimal portfolio allocations, engaging in risk management and forecasting future volatility in equity and commodity markets.     

Testing volatility persistence on Markov switching stochastic volatility models

In the literature, some researchers found that the high persistence of the volatility can be caused by Markov regime switching. This concern can be reflected as a unit root problem on the basis of Markov switching models. In this paper, our main purpose is to provide a Bayesian unit root testing approach for Markov switching stochastic volatility (MSSV) models. We illustrate the developed approach using S&P 500 daily return covering the subprime crisis started in 2008.     

Forecasting volatility of futures market: the S&P 500 and FTSE 100 futures using high frequency returns and implied volatility

We show that historical volatility from high frequency returns outperforms implied volatility when standardized returns by historical volatility tends to be normally distributed. For the FTSE 100 futures, we find that historical volatility using high frequency returns outperforms implied volatility in forecasting future volatility. However, we find that implied volatility outperforms historical volatility in forecasting future volatility for the S&P 500 futures. The results also indicate that historical volatility using high frequency returns could be an unbiased forecast for the FTSE 100 futures.     

Analysis of contagion from the dynamic conditional correlation model with Markov Regime switching

Over the last decades, the transmissions of international financial events have been the subject of many academic studies focused on multivariate volatility models. This study evaluates the financial contagion between stock market returns. The econometric model employed, regime switching dynamic correlation (RSDC). A modification was made in the original RSDC model, the introduction of the GJR-GARCH-N and also GJR-GARCH-t models, on the equation of conditional univariate variances, thus allowing us to capture the asymmetric effects in volatility and also heavy tails. A database was built using series of indices in the United States (S&P500), the United Kingdom (FTSE100), Brazil (IBOVESPA) and South Korea (KOSPI) from 1 February 2003 to 20 September 2012. Throughout this study the methodology is compared with those frequently found in literature, and the model RSDC with two regimes was defined as the most appropriate for the selected sample with t-Student distribution in the disturbances. The adapted RSDC model used in this article can be used to detect contagion – considering the definition of financial contagion from the World Bank called very restrictive – with the help of the empirical exercise.     

On the asymmetric impact of macro–variables on volatility

We extend the GARCH–MIDAS model to take into account possible different impacts from positive and negative macroeconomic variations on financial market volatility: a Monte Carlo simulation which shows good properties of the estimator with realistic sample sizes. The empirical application is performed on the daily S&P500 volatility dynamics with the U.S. monthly industrial production and national activity index as additional (signed) determinants. We estimate the Relative Marginal Effect of macro variable movements on volatility at different lags. In the out-of-sample analysis, our proposed GARCH–MIDAS model not only statistically outperforms the competing specifications (GARCH, GJR-GARCH and GARCH–MIDAS models), but shows significant utility gains for a mean-variance investor under different risk aversion parameters. Attention to robustness is given by choosing different samples and estimating the model in an international context (six different stock markets).     

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.     

Evaluating and improving GARCH-based volatility forecasts with range-based estimators

This article investigates the feasibility of using range-based estimators to evaluate and improve Generalized Autoregressive Conditional Heteroscedasticity (GARCH)-based volatility forecasts due to their computational simplicity and readily availability. The empirical results show that daily range-based estimators are sound alternatives for true volatility proxies when using Superior Predictive Ability (SPA) test of Hansen (2005) to assess GARCH-based volatility forecasts. In addition, the inclusion of the range-based estimator of Garman and Klass (1980) can significantly improve the forecasting performance of GARCH-t model.     

A discussion on the innovation distribution of the Markov regime-switching GARCH model

The Markov Regime-Switching Generalized autoregressive conditional heteroskedastic (MRS-GARCH) model is a widely used approach to model the financial volatility with potential structural breaks. The original innovation of the MRS-GARCH model is assumed to follow the Normal distribution, which cannot accommodate fat-tailed properties commonly existing in financial time series. Many existing studies point out that this problem can lead to inconsistent estimates. To overcome it, the Student's t-distribution and General Error Distribution (GED) are the two most popular alternatives. However, a recent study points out that the Student's t-distribution lacks stability. Also, it incorporates the α-stable distribution in the GARCH-type model. The issue of the α-stable distribution is that its second moment does not exist. To solve this problem, the tempered stable distribution, which retains most characteristics of the α-stable distribution and has defined moments, is a natural candidate. In this paper, we conduct a series of simulation studies to demonstrate that MRS-GARCH model with tempered stable distribution consistently outperform that with Student's t-distribution and GED. Our empirical study on the S&P 500 daily return volatility also generates robust results. Therefore, we argue that the tempered stable distribution could be a widely useful tool for modeling the financial volatility in general contexts with a MRS-GARCH-type specification.     

Which types of commodity price information are more useful for predicting US stock market volatility?

This study aims to investigate which types of commodity price information are more useful for predicting US stock market realized volatility (RV) in a data-rich word. The standard predictive regression framework and monthly RV data are used to explore the RV predictability of commodity futures for the next-month RV on S&P 500 spot index. We utilize principal component analysis (PCA) and factor analysis (FA) to extract the common factors for each type and all types of commodity futures. Our results indicate that the futures volatility information of grains and softs has a significant predictive ability in forecasting the RV of the S&P 500. In addition, the FA method can yield better forecasts than the PCA and average methods in most cases. Further analysis shows that the volatility information of grains and softs exhibits higher informativeness during recessions and pre-crises. Finally, the forecasts of the five combination methods and different out-of-sample periods confirm our results are robust.     

Volatility spillover and multivariate volatility impulse response analysis of GFC news events

This article applies two measures to assess spillovers across markets: the Diebold and Yilmaz’s (2012) spillover index and the Hafner and Herwartz’s (2006) analysis of multivariate GARCH models using volatility impulse response analysis. We use two sets of data, daily realized volatility (RV) estimates taken from the Oxford-Man RV library, for the S&P500 and the FTSE, plus 10 years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index. Both data sets capture both the global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The spillover index captures the transmission of volatility to and from markets, plus net spillovers. The Volatility Impulse Responses (VIRF) have to be calibrated to conditional volatility estimated at a particular point in time. We explore the impact of three different shocks, the onset of the GFC, the height of the GFC, and the impact of the ESDC. Our modelling includes leverage and asymmetric effects applying a multivariate GARCH model, and further analysis using both BEKK and diagonal BEKK (DBEKK) models. We find the impact of negative shocks is larger, but shorter in duration, in this case a difference between 3 and 6 months.     

Modeling volatility and conditional correlations between socially responsible investments,gold and oil

Socially responsible investing (SRI) is one of the fastest growing areas of investing. While there is a considerable literature comparing SRI to various benchmarks, very little is known about the volatility dynamics of socially responsible investing. In this paper, multivariate GARCH models are used to model volatilities and conditional correlations between a stock price index comprised of socially responsible companies, oil prices, and gold prices. The dynamic conditional correlation model is found to fit the data the best and used to generate dynamic conditional correlations, hedge ratios and optimal portfolio weights. From a risk management perspective, SRI offers very similar results in terms of dynamic conditional correlations, hedge ratios, and optimal portfolio weights as investing in the S&P 500. For example, SRI investors can expect to pay a similar amount to hedge their investment with oil or gold as investors in the S&P 500 would pay. These results can help investors and portfolio managers make more informed investment decisions.     

Nonparametric estimation of stochastic volatility models

This letter introduces nonparametric estimators of the drift and diffusion coefficient of stochastic volatility models which exploit techniques for estimating integrated volatility with high-frequency data. The performance of the proposed estimators is assessed on simulations of two popular stochastic volatility models.     

Revisiting the long memory dynamics of the implied–realized volatility relationship: New evidence from the wavelet regression

The literature studying stock index options confirms severe biases and inefficiencies in using implied volatility as a forecast of future volatility. In this paper, we revisit the implied–realized volatility relationship with wavelet band least squares (WBLS) exploring the long memory of volatility, a possible cause of the bias. Using the S&P 500 and DAX monthly and bi-weekly option prices covering the recent financial crisis, we conclude that the implied–realized volatility relation is driven solely by the lower frequencies of the spectra representing long investment horizons. The findings enable improvement of future volatility forecasts as they support unbiasedness of implied volatility as a good proxy for future volatility in the long run.     

Modeling volatility with time-varying FIGARCH models

This paper puts the light on a new class of time-varying FIGARCH or TV-FIGARCH processes to model the volatility. This new model has the feature to account for the long memory and the structural change in the conditional variance process. The structural change is modeled by a logistic function allowing the intercept to vary over time. We also implement a modeling strategy for our TV-FIGARCH specification whose performance is examined by a Monte Carlo study. An empirical application to the crude oil price and the S&P 500 index is carried out to illustrate the usefulness of our techniques. The main result of this paper is that the long memory behavior of the absolute returns is not only explained by the existence of the long memory in the volatility but also by deterministic changes in the unconditional variance.     

Implied correlation indices and volatility forecasting

Implied volatility indices are an important measure for ‘market fear’ and well-known in academia and practice. Correlation is still paid less attention even though the CBOE started to calculate implied correlation indices for the S&P500 in 2009. However, the literature especially on cross-country dependencies and applications is still quite thin. We are closing this gap by constructing an implied correlation index for the DAX and taking a deeper look at the (intercontinental) relationship between equity, volatility and correlation indices. Additionally, we show that implied correlation could improve implied volatility forecasting.     

Aggregation and long-memory: An analysis based on the discrete Fourier transform

Datasets constructed via temporal aggregation or skip sampling are widely used by empirical studies in economics and finance, which leads to substantive discussion and debates on the effects of temporal aggregation and choice of sampling frequency. This paper studies a key feature of data aggregation by deriving the representation of the discrete Fourier transform (dft) of the aggregated series considering the aliasing effect. Analyses are not limited to the spectrum of the stationary series under aggregation, but extended to the periodogram of the non-stationary series. We further apply our results of the dft to a particular example of fractional processes under aggregation. We show that the estimates of the long-memory parameter are the same for the temporally aggregated series and the original one if the same bandwidths are used, regardless of the stationarity of the series. The theoretical findings are empirically verified by the analysis of S&P 500 volatility from 1928 to 2011.     

Dynamic hedge ratio for stock index futures: application of threshold VECM

This study represents one of the first papers in stock-index-futures arbitrage literature to investigate the effects of arbitrage threshold on stock index futures hedging effectiveness by using threshold vector error correction model (hereafter threshold VECM). Moreover, in contrast to prior studies focusing on examining case studies involving mature stock markets, this study not only adopts US S&P 500 stock market as the sample but also adds an analysis of one emerging stock market, Hungarian BSI and examines the differences between them. Finally, this investigation employs a rolling estimation process to examine the impact of arbitrage threshold behaviours on the setting of futures hedging ratio. The empirical findings of this study are consistent with the following notions. First, arbitrage behaviour reduces co-movement between futures and spot markets and increases the volatility of both futures and spot markets. Second, this article denotes the outer regime of futures-spot market for the case of Hungarian BSI (US S&P 500) as a crisis (an unusual) condition. Moreover, arbitrage threshold behaviours make remarkable (unremarkable) shift on optimal hedge ratio between two different market regimes for the case of Hungarian BSI (US S&P 500). Finally, the framework involving regime-varying hedge ratio designed in this study provides a more efficient futures hedge ratio design for Hungarian BSI stock market, but not for US S&P 500 stock market.     

QARMA-Beta-t-EGARCH versus ARMA-GARCH: an application to S&P 500

Statistical performance and out-of-sample forecast precision of ARMA-GARCH and QARMA-Beta-t-EGARCH are compared. We study daily returns on the Standard and Poor’s 500 (S&P 500) index and a random sample of 50 stocks from the S&P 500 for period May 2006 to July 2010. Competing models are estimated for periods before and during the US financial crisis of 2008. Out-of-sample point and density forecasts are performed for periods during and after the US financial crisis. The results provide evidence of the superior in-sample statistical and out-of-sample predictive performance of QARMA-Beta-t-EGARCH.