Value at risk estimation by threshold stochastic volatility model

This article proposes a threshold stochastic volatility model that generates volatility forecasts specifically designed for value at risk (VaR) estimation. The method incorporates extreme downside shocks by modelling left-tail returns separately from other returns. Left-tail returns are generated with a t-distributional process based on the historically observed conditional excess kurtosis. This specification allows VaR estimates to be generated with extreme downside impacts, yet remains empirically widely applicable. This article applies the model to daily returns of seven major stock indices over a 22-year period and compares its forecasts to those of several other forecasting methods. Based on back-testing outcomes and likelihood ratio tests, the new model provides reliable estimates and outperforms others.     

Uncertainty and crude oil market volatility: new evidence

ABSTRACT

The main goal of this paper is to investigate the predictability of five economic uncertainty indices for oil price volatility in a changing world. We employ the standard predictive regression framework, several model combination approaches, as well as two prevailing model shrinkage methods to evaluate the performances of the uncertainty indices. The empirical results based on simple autoregression models including only one index suggest that global economic policy uncertainty (GEPU) and US equity market volatility (EMV) indices have significant predictive power for crude oil market volatility. In addition, the model combination approaches adopted in this paper can improve slightly the performances of individual autoregressive models. Lastly, the two model shrinkage methods, namely Elastin net and Lasso, outperform other individual AR-type model and combination models in most forecasting cases. Other empirical results based on alternative forecasting methods, estimation window sizes, high/low volatility and economic expansion/recession time periods further make sure the robustness of our major conclusions. The findings in this paper also have several important economic implications for oil investors.     

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.     

Forecasting stock market volatility and information content of implied volatility index

This study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.     

Empirical Regularities of Financial Market Volatility and Good Modelling Process: Developing Countries’ Exchange Rate Markets Perspective

A survey of contemporary literature suggests that empirical studies on developing economies are few or almost non-existent. Engle and Patton (2001, What good is a volatility model. Quantitative Finance, 1, 237–245) as well as Poon (2005, A Practical Guide to Forecasting Financial Market Volatility. New Jersey: Wiley.) suggest that a good volatility model is one that utilizes the empirical regularities of financial market volatility (of which most were observed on industrialized economies markets). This paper uses exchange rate series from Ghana, Mozambique and Tanzania to show that;

1. they are not different from other financial markets as they exhibit most of the empirical regularities including volatility sign asymmetry, non-normal distribution and volatility clustering. It is however observed that the three exchange rate series are very volatile, with induced volatile shocks highly persistent and asymmetric, and extreme prices commonplace;

2. the ARCH technique (which has been well documented to capture these empirical regularities and produce good forecasts) generally produced a good fit to the three exchange rate series when compared with volatility forecasts generated using the EWMA technique. In the simple analysis of a day-ahead volatility forecast abilities of estimated models, it was observed that best fit does not necessarily ensure best forecast.

     

Predictive ability of asymmetric volatility models at medium-term horizons

Using realized volatility to estimate conditional variance of financial returns, we compare forecasts of volatility from linear GARCH models with asymmetric ones. We consider horizons extending to 30 days. Forecasts are compared using three different evaluation tests. With data from an equity index and two foreign exchange returns, we show that asymmetric models provide statistically significant forecast improvements upon the GARCH model for two of the datasets and improve forecasts for all datasets by means of forecasts combinations. These results extend to about 10 days in the future, beyond which the forecasts are statistically inseparable from each other.     

Backtesting expected shortfall: evidence from European securitized real estate

Events such as the European sovereign debt crisis, terrorism and Brexit cause more uncertainty and volatility in capital markets. This encourages us to use both conditional and unconditional forecasts (backtests) for expected shortfall (ES) in 8 indices of listed European real estate securities and Real estate investment trusts (REITs). Using the method proposed by Du and Escanciano, we find that ES is generally superior to Value-at-Risk in describing and capturing risk during extreme events such as the financial crisis. Our results are important to regulators, risk managers and investors.     

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.     

QUANTILE FORECASTS OF FINANCIAL RETURNS USING REALIZED GARCH MODELS*

This article applies the realized generalized autoregressive conditional heteroskedasticity (GARCH) model, which incorporates the GARCH model with realized volatility, to quantile forecasts of financial returns, such as Value‐at‐Risk and expected shortfall. Student's t‐ and skewed Student's t‐distributions as well as normal distribution are used for the return distribution. The main results for the S&P 500 stock index are: (i) the realized GARCH model with the skewed Student's t‐distribution performs better than that with the normal and Student's t‐distributions and the exponential GARCH model using the daily returns only; and (ii) using the realized kernel to take account of microstructure noise does not improve the performance.     

FORECASTING GLOBAL EQUITY INDICES USING LARGE BAYESIAN VARS

This paper proposes a large Bayesian Vector Autoregressive (BVAR) model with common stochastic volatility to forecast global equity indices. Using a monthly dataset on global stock indices, the BVAR model controls for co‐movement commonly observed in global stock markets. Moreover, the time‐varying specification of the covariance structure accounts for sudden shifts in the level of volatility. In an out‐of‐sample forecasting application we show that the BVAR model with stochastic volatility significantly outperforms the random walk both in terms of point as well as density predictions. The BVAR model without stochastic volatility, on the other hand, shows some merits relative to the random walk for forecast horizons greater than six months ahead. In a portfolio allocation exercise we moreover provide evidence that it is possible to use the forecasts obtained from our model with common stochastic volatility to set up simple investment strategies. Our results indicate that these simple investment schemes outperform a naive buy‐and‐hold strategy.     

Improving GARCH volatility forecasts with regime-switching GARCH

Many researchers use GARCH models to generate volatility forecasts. Using data on three major U.S. dollar exchange rates we show that such forecasts are too high in volatile periods. We argue that this is due to the high persistence of shocks in GARCH forecasts. To obtain more flexibility regarding volatility persistence, this paper generalizes the GARCH model by distinguishing two regimes with different volatility levels; GARCH effects are allowed within each regime. The resulting Markov regime-switching GARCH model improves on existing variants, for instance by making multi-period-ahead volatility forecasting a convenient recursive procedure. The empirical analysis demonstrates that the model resolves the problem with the high single-regime GARCH forecasts and that it yields significantly better out-of-sample volatility forecasts. First Version Received: November 2000/Final Version Received: August 2001     

Modeling and forecasting return jumps using realized variation measures

This paper proposes a simple HAR-RV-based model to predict return jumps through a conditional density of jump size with time-varying moments. We model jump occurrences based on a version of the autoregressive conditional hazard model that relies on past continuous realized volatilities. Applying our methodology to seven equity indices on the U.S. and Chinese stock markets, we reach the following key findings: (i) jump occurrence and size are dependent on past realized volatility, (ii) the proposed model yields superior in- and out-of-sample jump size density forecasts compared to an ARMA(1,1)-GARCH(1,1) model, (iii) and the occurrence and sign of return jumps are predictable to some extent.     

Relationships among U.S. oil prices and oil industry equity indices

The cointegration analysis suggests that the pure oil industry equity system and the mixed oil price/equity index system offers more opportunities for long-run portfolio diversification and less market integration than the pure oil price systems. On a daily basis, in the oil price systems all oil prices with the exception of the 3-month futures can explain the future movements of each other. In the mixed system, none of the daily oil industry stock indices can explain the daily future movements of the New York Mercantile Exchange (NYMEX) futures prices, whereas these prices can explain the movements of independent companies engaged in exploration, refining, and marketing. The spillover analysis of oil volatility transmission suggests that the oil futures market has a matching or echoing volatility effect on the stocks of some oil sectors and a volatility-dampening effect on the stocks of others. The policy implication is that, during times of high oil volatility, traders should choose the S&P oil sector stocks that match their tolerance for volatility and use the right financial derivative to hedge against or profit from this volatility. The day effect for volatility transmission suggests that Friday has a calming effect on the volatility of oil stocks in general. The effect for Monday is not significant.     

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.     

Coordination and correlation in Markov rational belief equilibria

Summary This paper studies the effect of correlation in the rational beliefs of agents on the volatility of asset prices. We use the technique of generating variables to study stable and non-stationary processes needed to characterize rational beliefs. We then examine how the stochastic interaction among such variables affects the behavior of a wide class of Rational Belief Equilibria (RBE). The paper demonstrates how to construct a consistent price state space and then shows the existence of RBE for any economy for which such price state space is constructed. Next, the results are used to study the volatility of asset prices via numerical simulation of a two agents model. If beliefs of agents are uniformly dispersed and independent, we would expect heterogeneity of beliefs to have a limited impact on the fluctuations of asset prices. On the other hand, our results show that correlation across agents can have a complex and dramatic effect on the volatility of prices and thus can be the dominant factor in the fluctuation of asset prices. The mechanism generating this effect works through the clustering of beliefs in states of different levels of agreement. In states of agreement the conditional forecasts of the agents tend to fluctuatetogether inducing more volatile asset prices. In states of disagreement the conditional forecasts fluctuatein diverse directions tending to cancel each other's effect on market demand and resulting in reduced price volatility.This research was supported, in part, by the Fondazione Eni Enrico Mattei of Milan, Italy, and by the Research Incentive Fund of Stanford University. The authors thank Carsten K. Nielsen and Ho-Mou Wu for valuable discussions on an earlier draft. Carsten K. Nielsen also made an important contribution to the development of Section 3.     

Multi-horizon inflation forecasts using disaggregated data

In this paper we use multi-horizon evaluation techniques to produce monthly inflation forecasts for up to twelve months ahead. The forecasts are based on individual seasonal time series models that consider both, deterministic and stochastic seasonality, and on disaggregated Consumer Price Index (CPI) data. After selecting the best forecasting model for each index, we compare the individual forecasts to forecasts produced using two methods that aggregate hierarchical time series, the bottom-up method and an optimal combination approach. Applying these techniques to 16 indices of the Mexican CPI, we find that the best forecasts for headline inflation are able to compete with those taken from surveys of experts.     

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.     

Does international oil volatility have directional predictability for stock returns? Evidence from BRICS countries based on cross-quantilogram analysis

While numerous studies have investigated the relationship between oil volatility and stock returns, it is surprising that little research has examined the quantile dependence and directional predictability from oil volatility to stock returns in BRICS (Brazil, Russia, India, China, and South Africa) countries. We address this issue by using the cross-quantilogram model proposed by Han et al. (2016). The empirical results show that, overall, oil volatility has a directional predictability for the stock returns in BRICS countries. When the oil volatility is in a low quantile (lower than its 0.1 quantiles), it is less likely to show either a large loss or a large gain in the stock market. In contrast, there is an increased likelihood of either large loss or a large gain in the stock market when the oil volatility is in a high quantile (higher than its 0.9 quantiles). The directional predictability from the oil volatility to stock returns depends on the net position of oil imports and exports of these BRICS countries in the oil market. The net oil exporters (Russia and Brazil) are less likely to have large gains and large losses in the stock market than are the net oil importers (India, China, and South Africa) when the oil volatility is in a low quantile. The net oil exporters are more likely to have large gains and large losses than are the net oil importers when the oil volatility is in a high quantile. The results are robust to change in the variable of oil volatility and the sample interval.     

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.     

Forecasting the oil futures price volatility: A new approach

This study provides a new perspective of modelling and forecasting realized range-based volatility (RRV) for crude oil futures. We are the first to improve the Heterogeneous Autoregressive model of Realized Range-based Volatility (HAR-RRV) model by considering the significant jump components, signed returns and volatility of realized range-based volatility. The empirical results show that the volatility of volatility significantly exists in the oil futures market. Moreover, our new proposed models with significant jump components, signed returns and volatility of volatility can gain higher forecast accuracy than HAR-RRV-type models. The results are robust to different forecasting windows and forecasting horizons. Our new findings are strategically important for investors making better decisions.