Forecasting volatility of the U.S. oil market

We examine the information content of the CBOE Crude Oil Volatility Index (OVX) when forecasting realized volatility in the WTI futures market. Additionally, we study whether other market variables, such as volume, open interest, daily returns, bid-ask spread and the slope of the futures curve, contain predictive power beyond what is embedded in the implied volatility. In out-of-sample forecasting we find that econometric models based on realized volatility can be improved by including implied volatility and other variables. Our results show that including implied volatility significantly improves daily and weekly volatility forecasts; however, including other market variables significantly improves daily, weekly and monthly volatility forecasts.     

Components of Market Risk and Return

This article proposes a flexible but parsimonious specificationof the joint dynamics of market risk and return to produce forecastsof a time-varying market equity premium. Our parsimonious volatilitymodel allows components to decay at different rates, generatesmean-reverting forecasts, and allows variance targeting. Thesefeatures contribute to realistic equity premium forecasts forthe U.S. market over the 1840–2006 period. For example,the premium forecast was low in the mid-1990s but has recentlyincreased. Although the market's total conditional variancehas a positive effect on returns, the smooth long-run componentof volatility is more important for capturing the dynamics ofthe premium. This result is robust to univariate specificationsthat condition on either levels or logs of past realized volatility(RV), as well as to a new bivariate model of returns and RV.     

Forecasting financial market volatility: Sample frequency vis-à-vis forecast horizon

This paper explores the return volatility predictability inherent in high-frequency speculative returns. Our analysis focuses on a refinement of the more traditional volatility measures, the integrated volatility, which links the notion of volatility more directly to the return variance over the relevant horizon. In our empirical analysis of the foreign exchange market the integrated volatility is conveniently approximated by a cumulative sum of the squared intraday returns. Forecast horizons ranging from short intraday to 1-month intervals are investigated. We document that standard volatility models generally provide good forecasts of this economically relevant volatility measure. Moreover, the use of high-frequency returns significantly improves the longer run interdaily volatility forecasts, both in theory and practice. The results are thus directly relevant for general research methodology as well as industry applications.     

The bias in Black-Scholes/Black implied volatility: An analysis of equity and energy markets

In this paper we examine the extent of the bias between Black and Scholes (1973)/Black (1976) implied volatility and realized term volatility in the equity and energy markets. Explicitly modeling a market price of volatility risk, we extend previous work by demonstrating that Black-Scholes is an upward-biased predictor of future realized volatility in S&P 500/S&P 100 stock-market indices. Turning to the Black options-on-futures formula, we apply our methodology to options on energy contracts, a market in which crises are characterized by a positive correlation between price-returns and volatilities: After controlling for both term-structure and seasonality effects, our theoretical and empirical findings suggest a similar upward bias in the volatility implied in energy options contracts. We show the bias in both Black-Scholes/Black implied volatilities to be related to a negative market price of volatility risk. JEL Classification G12 · G13     

Good volatility,bad volatility,and the cross section of cryptocurrency returns

This paper examines the predictability of realized volatility measures (RVM), especially the realized signed jumps (RSJ), on future volatility and returns. We confirm the existence of volatility persistence and future volatility is more strongly related to the volatility of past positive returns than to that of negative returns in the cryptocurrency market. RSJ-sorted cryptocurrency portfolios yield statistically and economically significant differences in the subsequent portfolio returns. After controlling for cryptocurrency market characteristics and existing risk factors, the differences remain significant. The investor attention explains the predictability of realized jump risk in future cryptocurrency returns.     

基于“已实现”波动率的ARFIMA模型预测实证研究

本文采用二次移动平均方法平衡影响"已实现"波动率预测精度的测量误差和市场微观结构误差,利用沪深300指数高频数据实证研究,结果表明"已实现"波动率序列的分布是非正态分布且具有长记忆性,对数"已实现"波动率序列接近于正态分布;最后建立ARFIMA模型,并对波动率进行了预测研究。     

Forecasting oil price realized volatility using information channels from other asset classes

Motivated from Ross (1989) who maintains that asset volatilities are synonymous to the information flow, we claim that cross-market volatility transmission effects are synonymous to cross-market information flows or “information channels” from one market to another. Based on this assertion we assess whether cross-market volatility flows contain important information that can improve the accuracy of oil price realized volatility forecasting. We concentrate on realized volatilities derived from the intra-day prices of the Brent crude oil and four different asset classes (Stocks, Forex, Commodities and Macro), which represent the different “information channels” by which oil price volatility is impacted from. We employ a HAR framework and estimate forecasts for 1-day to 66-days ahead. Our findings provide strong evidence that the use of the different “information channels” enhances the predictive accuracy of oil price realized volatility at all forecasting horizons. Numerous forecasting evaluation tests and alternative model specifications confirm the robustness of our results.     

Asymmetric volatility in the foreign exchange markets

We examine the presence or absence of asymmetric volatility in the exchange rates of Australian dollar (AUD), Euro (EUR), British pound (GBP) and Japanese yen (JPY), all against US dollar. Our investigation is based on a variant of the heterogeneous autoregressive realized volatility model, using daily realized variance and return series from 1996 to 2004. We find that a depreciation against USD leads to significantly greater volatility than an appreciation for AUD and GBP, whereas the opposite is true for JPY. Relative to volatility on days following a positive one-standard-deviation return, volatility on days following a negative one-standard-deviation return is higher by 6.6% for AUD, 6.1% for GBP, and 21.2% for JPY. The realized volatility of EUR appears to be symmetric. These results are robust to the removal of jump component from realized volatility and the sub-samplings defined by structural-changes. The asymmetry in AUD, GBP and JPY appears to be embedded in the continuous component of realized volatility rather than the jump component.     

‘Déjà vol’: Predictive regressions for aggregate stock market volatility using macroeconomic variables

Aggregate stock return volatility is both persistent and countercyclical. This paper tests whether it is possible to improve volatility forecasts at monthly and quarterly horizons by conditioning on additional macroeconomic variables. I find that several variables related to macroeconomic uncertainty, time-varying expected stock returns, and credit conditions Granger cause volatility. It is more difficult to find evidence that forecasts exploiting macroeconomic variables outperform a univariate benchmark out-of-sample. The most successful approaches involve simple combinations of individual forecasts. Predictive power associated with macroeconomic variables appears to concentrate around the onset of recessions.     

The relationship between implied and realized volatility: evidence from the Australian stock index option market

This paper examines the relationship between the volatility implied in option prices and the subsequently realized volatility by using the S&P/ASX 200 index options (XJO) traded on the Australian Stock Exchange (ASX) during a period of 5 years. Unlike stock index options such as the S&P 100 index options in the US market, the S&P/ASX 200 index options are traded infrequently and in low volumes, and have a long maturity cycle. Thus an errors-in-variables problem for measurement of implied volatility is more likely to exist. After accounting for this problem by instrumental variable method, it is found that both call and put implied volatilities are superior to historical volatility in forecasting future realized volatility. Moreover, implied call volatility is nearly an unbiased forecast of future volatility.

The role of jumps and leverage in forecasting volatility in international equity markets

We analyze the importance of jumps and the leverage effect on forecasts of realized volatility in a large cross-section of 18 international equity markets, using daily realized measures data from the Oxford-Man Realized Library, and two widely employed empirical models for realized volatility that allow for jumps and leverage. Our out-of-sample forecast evaluation results show that the separation of realized volatility into a continuous and a discontinuous (jump) component is important for the S&P 500, but of rather limited value for the remaining 17 international equity markets that we analyze. Only for 6 equity markets are significant and sizable forecast improvements realized at the one-step-ahead horizon, which, nevertheless, deteriorate quickly and abruptly as the prediction horizon increases. The inclusion of the leverage effect, on the other hand, has a much larger impact on all 18 international equity markets. Forecast gains are not only highly significant, but also sizeable, with gains remaining significant for forecast horizons of up to one month ahead.     

The information content of risk-neutral skewness for volatility forecasting

The paper investigates whether risk-neutral skewness has incremental explanatory power for future volatility in the S&P 500 index. While most of previous studies have investigated the usefulness of historical volatility and implied volatility for volatility forecasting, we study the information content of risk-neutral skewness in volatility forecasting model. In particular, we concentrate on Heterogeneous Autoregressive model of Realized Volatility and Implied Volatility (HAR-RV-IV). We find that risk-neutral skewness contains additional information for future volatility, relative to past realized volatilities and implied volatility. Out-of-sample analyses confirm that risk-neutral skewness improves significantly the accuracy of volatility forecasts for future volatility.     

The information content of option-implied information for volatility forecasting with investor sentiment

This study explores the effect of investor sentiment on the volatility forecasting power of option-implied information. We find that the risk-neutral skewness has the explanatory power regarding future volatility only during high sentiment periods. Furthermore, the implied volatility has varying volatility forecasting ability depending on the level of investor sentiment. Our findings suggest that the effectiveness of volatility forecasting models based on option-implied information varies over time with the level of investor sentiment. We confirm the important role of investor sentiment in volatility forecasting models exploiting option-implied information with strong evidence from in-sample and out-of-sample analyses. We also present improvements in the accuracy of volatility forecasts from volatility forecasting models derived by incorporating investor sentiment in these models.     

Do fear indices help predict stock returns?

This study investigates the forecasting power of implied volatility indices on forward looking returns. Prior studies document that negative innovations to returns are associated with increasing implied volatility of the underlying indices; thus, suggesting a possible relationship between extremely high levels of implied volatility and positive short term returns. We investigate this issue by examining the predictive power of three implied volatility indices, VIX, VXN and VDAX, on the underlying index returns. We extend previous research by also focusing on characterised selected stocks and examine the relationship between implied volatility indices and future returns across different sectors and classified portfolios. Our findings suggest that implied volatility indices are good predictors of 20-days and 60-days forward looking returns and illustrate insignificant predictive power for very short term (1-day and 5-days) returns.     

The one-trading-day-ahead forecast errors of intra-day realized volatility

Two volatility forecasting evaluation measures are considered; the squared one-day-ahead forecast error and its standardized version. The mean squared forecast error is the widely accepted evaluation function for the realized volatility forecasting accuracy. Additionally, we explore the forecasting accuracy based on the squared distance of the forecast error standardized with its volatility. The statistical properties of the forecast errors point the standardized version as a more appropriate metric for evaluating volatility forecasts.We highlight the importance of standardizing the forecast errors with their volatility. The predictive accuracy of the models is investigated for the FTSE100, DAX30 and CAC40 European stock indices and the exchange rates of Euro to British Pound, US Dollar and Japanese Yen. Additionally, a trading strategy defined by the standardized forecast errors provides higher returns compared to the strategy based on the simple forecast errors. The exploration of forecast errors is paving the way for rethinking the evaluation of ultra-high frequency realized volatility models.     

Asset volatility

We examine whether fundamental measures of volatility are incremental to market-based measures of volatility in (i) predicting bankruptcies (out of sample), (ii) explaining cross-sectional variation in credit spreads, and (iii) explaining future credit excess returns. Our fundamental measures of volatility include (i) historical volatility in profitability, margins, turnover, operating income growth, and sales growth; (ii) dispersion in analyst forecasts of future earnings; and (iii) quantile regression forecasts of the interquartile range of the distribution of profitability. We find robust evidence that these fundamental measures of volatility improve out-of-sample forecasts of bankruptcy and help explain cross-sectional variation in credit spreads. This suggests that an analysis of credit risk can be enhanced with a detailed analysis of fundamental information. As a test case of the benefit of volatility forecasting, we document an improved ability to forecast future credit excess returns, particularly when using fundamental measures of volatility.     

Is volatility clustering of asset returns asymmetric?

Volatility clustering is a well-known stylized feature of financial asset returns. This paper investigates asymmetric pattern in volatility clustering by employing a univariate copula approach of Chen and Fan (2006). Using daily realized kernel volatilities constructed from high frequency data from stock and foreign exchange markets, we find evidence that volatility clustering is highly nonlinear and strongly asymmetric in that clusters of high volatility occur more often than clusters of low volatility. To the best of our knowledge, this paper is the first one to address and uncover this phenomenon. In particular, the asymmetry in volatility clustering is found to be more pronounced in the stock markets than in the foreign exchange markets. Further, the volatility clusters are shown to remain persistent for over a month and asymmetric across different time periods. Our findings have important implications for risk management. A simulation study indicates that models which accommodate asymmetric volatility clustering can significantly improve the out-of-sample forecasts of Value-at-Risk.     

Quantile forecasts of daily exchange rate returns from forecasts of realized volatility

Quantile forecasts are central to risk management decisions because of the widespread use of Value-at-Risk. A quantile forecast is the product of two factors: the model used to forecast volatility, and the method of computing quantiles from the volatility forecasts. In this paper we calculate and evaluate quantile forecasts of the daily exchange rate returns of five currencies. The forecasting models that have been used in recent analyses of the predictability of daily realized volatility permit a comparison of the predictive power of different measures of intraday variation and intraday returns in forecasting exchange rate variability. The methods of computing quantile forecasts include making distributional assumptions for future daily returns as well as using the empirical distribution of predicted standardized returns with both rolling and recursive samples. Our main findings are that the Heterogenous Autoregressive model provides more accurate volatility and quantile forecasts for currencies which experience shifts in volatility, such as the Canadian dollar, and that the use of the empirical distribution to calculate quantiles can improve forecasts when there are shifts.     

Correlated implied volatility with jump and cross section of stock returns

I derive the option‐implied volatility allowing for nonzero correlation between price jump and diffusive risk to examine the information content of implied diffusive, jump risks and their implied covariance in the cross‐sectional variation of future returns. This study documents a strong predictive power of realized volatility and correlated implied volatility spread (RV ? IV_C) in the cross section of stock returns. The difference of realized volatility with the implied diffusive volatility (RV ? σ_C), jump risk (RV ? γ_C) and covariance (RV ? ICov) can forecast future returns. These RV ? σ_C and RV ? γ_C anomalies are robustly persistent even after controlling for market, size, book‐to‐market value, momentum and liquidity factors.