The quality of market volatility forecasts implied by S&P 100 index option prices

This study examines the performance of the S&P 100 implied volatility as a forecast of future stock market volatility. The results indicate that the implied volatility is an upward biased forecast, but also that it contains relevant information regarding future volatility. The implied volatility dominates the historical volatility rate in terms of ex ante forecasting power, and its forecast error is orthogonal to parameters frequently linked to conditional volatility, including those employed in various ARCH specifications. These findings suggest that a linear model which corrects for the implied volatility's bias can provide a useful market-based estimator of conditional volatility.     

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.

Forecasting stock market volatility and the informational efficiency of the DAX-index options market

Alternative strategies for predicting stock market volatility are examined. In out-of-sample forecasting experiments implied-volatility information, derived from contemporaneously observed option prices or history-based volatility predictors, such as GARCH models, are investigated to determine if they are more appropriate for predicting future return volatility. Employing German DAX-index return data it is found that past returns do not contain useful information beyond the volatility expectations already reflected in option prices. This supports the efficient market hypothesis for the DAX-index options market.     

The relation between implied and realised volatility in the Danish option and equity markets

We show that the conclusions to be drawn concerning the informational efficiency of illiquid options markets depend critically on whether one carefully recognises and appropriately deals with the econometrics of the errors‐in‐variables problem. This paper examines the information content of options on the Danish KFX share index. We consider the relation between the volatility implied in an option's price and the subsequently realised index return volatility. Since these options are traded infrequently and in low volumes, the errors‐in‐variables problem is potentially large. We address the problem directly using instrumental variables techniques. We find that when measurement errors are controlled for, call option prices even in this very illiquid market contain information about future realised volatility over and above the information contained in historical volatility.     

The importance of the volatility risk premium for volatility forecasting

In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20 years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.     

Local and spillover shocks in implied market volatility: evidence for the U.S. and Germany

The occurrence and the transmission of large shocks in international equity markets is of essential interest to the study of market integration and financial crises. To this aim, implied market volatility allows to monitor ex ante risk expectations in different markets. We investigate the behavior of implied market volatility indices for the U.S. and Germany under a straightforward mean reversion model that allows for Poisson jumps. Our empirical findings for daily data in the period 1992 to 2002 provide evidence of significant positive jumps, i.e. situations of market stress with positive unexpected changes in ex ante risk assessments. Jump events are mostly country-specific with some evidence of volatility spillover. Analysis of public information around jump dates indicates two basic categories of events. First, crisis events occurring under spillover shocks. Second, information release events which include three subcategories, namely—worries about as well as actual—unexpected releases concerning U.S. monetary policy, macroeconomic data and corporate profits. Additionally, foreign exchange market movements may cause volatility shocks.     

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.     

Using implied volatility jumps for realized volatility forecasting: Evidence from the Chinese market

This study examines the Chinese implied volatility index (iVIX) to determine whether jump information from the index is useful for volatility forecasting of the Shanghai Stock Exchange 50ETF. Specifically, we consider the jump sizes and intensities of the 50ETF and iVIX as well as cojumps. The findings show that both the jump size and intensity of the 50ETF can improve the forecasting accuracy of the 50ETF volatility. Moreover, we find that the jump size and intensity of the iVIX provide no significant predictive ability in any forecasting horizon. The cojump intensity of the 50ETF and iVIX is a powerful predictor for volatility forecasting of the 50ETF in all forecasting horizons, and the cojump size is helpful for forecasting in short forecasting horizon. In addition, for a one-day forecasting horizon, the iVIX jump size in the cojump is more predictive of future volatility than that of the 50ETF when simultaneous jumps occur. Our empirical results are robust and consistent. This work provides new insights into predicting asset volatility with greater accuracy.     

Forecasting volatility in GARCH models with additive outliers

We model the volatility of a single risky asset using a multifactor (matrix) Wishart affine process, recently introduced in finance by Gourieroux and Sufana. As in standard Duffie and Kan affine models the pricing problem can be solved through the Fast Fourier Transform of Carr and Madan. A numerical illustration shows that this specification provides a separate fit of the long-term and short-term implied volatility surface and, differently from previous diffusive stochastic volatility models, it is possible to identify a specific factor accounting for the stochastic leverage effect, a well-known stylized fact of the FX option markets analysed by Carr and Wu.     

What is the correct meaning of implied volatility?

This paper presents a closed-form solution for the valuation of European options under the assumption that the excess returns of an underlying asset follow a diffusion process. In light of our model, the implied volatility computed from the Black–Scholes formula should be viewed as the volatility of excess returns rather than as the volatility of gross returns. Using the SPX and the OMX options data, we test whether implied volatility obtained from Black-Scholes option price explains the volatilities of excess returns better than gross returns, even though the result is not statistically significant.     

Investor sentiment and stock volatility: New evidence

This study investigates the predictability of sentiment measure on stock realized volatility. We propose a new investor sentiment index (NISI) based on the partial least squares method. This sentiment index outperforms many existing sentiment indicators in three aspects. First, in-sample result shows that the NISI has greater predictive power relative to the others. Most sentiment indicators show predictability in the non-crisis period only while the NISI is also effective in the crisis period. Furthermore, the NISI exhibits more prominent superiority in longer horizons forecasting. Second, further analysis indicates that the NISI has robust predictability before and after the Chinese stock market turbulence periods while the others not. Importantly, the NISI is still effective significantly after considering leverage effect while most of the others not. Finally, out-of-sample analysis demonstrates that the NISI is more powerful than other sentiment measures. This result is reproducible in different robustness checks.     

24-Hour realized volatilities and transatlantic volatility interdependence

This paper proposes an innovative econometric approach for the computation of 24-h realized volatilities across stock markets in Europe and the US. In particular, we deal with the problem of non-synchronous trading hours and intermittent high-frequency data during overnight non-trading periods. Using high-frequency data for the Euro Stoxx 50 and the S&P 500 Index between 2003 and 2011, we combine squared overnight returns and realized daytime variances to obtain synchronous 24-h realized volatilities for both markets. Specifically, we use a piece-wise weighting procedure for daytime and overnight information to take into account structural breaks in the relation between the two. To demonstrate the new possibilities that our approach opens up, we use the new 24-h volatilities to estimate a bivariate extension of Corsi et al.’s [Econom. Rev., 2008, 27(1–3), 46–78] HAR-GARCH model. The results suggest that the contemporaneous transatlantic volatility interdependence is remarkably stable over the sample period.     

Pricing under rough volatility

From an analysis of the time series of realized variance using recent high-frequency data, Gatheral et al. [Volatility is rough, 2014] previously showed that the logarithm of realized variance behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable timescale. The resulting Rough Fractional Stochastic Volatility (RFSV) model is remarkably consistent with financial time series data. We now show how the RFSV model can be used to price claims on both the underlying and integrated variance. We analyse in detail a simple case of this model, the rBergomi model. In particular, we find that the rBergomi model fits the SPX volatility markedly better than conventional Markovian stochastic volatility models, and with fewer parameters. Finally, we show that actual SPX variance swap curves seem to be consistent with model forecasts, with particular dramatic examples from the weekend of the collapse of Lehman Brothers and the Flash Crash.     

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.     

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.     

Spot and forward volatility in foreign exchange

This paper investigates the empirical relation between spot and forward implied volatility in foreign exchange. We formulate and test the forward volatility unbiasedness hypothesis, which may be viewed as the volatility analogue to the extensively researched hypothesis of unbiasedness in forward exchange rates. Using a new dataset of spot implied volatility quoted on over-the-counter currency options, we compute the forward implied volatility that corresponds to the delivery price of a forward contract on future spot implied volatility. This contract is known as a forward volatility agreement. We find strong evidence that forward implied volatility is a systematically biased predictor that overestimates movements in future spot implied volatility. This bias in forward volatility generates high economic value to an investor exploiting predictability in the returns to volatility speculation and indicates the presence of predictable volatility term premiums in foreign exchange.     

Which power variation predicts volatility well?

We estimate MIDAS regressions with various (bi)power variations to predict future volatility – measured via increments in quadratic variation. Instead of pre-determining the (bi)power variation we parameterize it and estimate the intra-daily return power transformation that optimally predicts future increments in quadratic variation. We find that the longer the prediction horizon, the smaller the optimal power transformation.     

Distilling private information from plain-vanilla options to predict future underlying stock price volatility: Evidence from the H-shares of Chinese banks

Deviations from put-call parity may arise in response to private information that a select group of investors possess. From a practical perspective, if one possesses private information, using options to speculate or hedge amplifies potential gains given the leverage embedded in options with respect to price changes in the underlying asset. In light of this, and if we assume that the average investor does not possess private information, it is perhaps possible though to infer such information through implied variance spreads and use it to predict future volatility in the underlying asset. In this piece I examine the extent to which such information is economically informative in predicting the intraday return variability of H-shares issued by China's state and joint-stock banks, respectively. Generally speaking, I uncover the following; firstly, call-put implied variance spreads are mean-reverting across time. Secondly, at any given point in time, the magnitude of the deviation from put-call parity is informative in predicting rises in future spot price volatility. Thirdly, straddle/strangle trades predict, at times one week in advance, rises in future spot price volatility. These findings hold after controlling for market-wide implied volatility, the flow and shock in information disseminating to the market, and implicit transactions costs.     

S&P 500 implied volatility and monetary policy announcements

While many studies have investigated the link between macroeconomic events and equity market volatility, few have considered the impact on option implied volatilities. Given the recent focus on trading in implied volatility, in the context of the S&P 500 VIX index, this paper examines how the VIX index behaves around US monetary policy announcements. It is revealed that the VIX index falls significantly on the day of Federal Open Market Committee meetings.     

Contemporaneous intraday volume, option, and futures volatility transmissions across parallel markets

The primary objective of this article is to investigate volatility transmission across three parallel markets operating on the Sydney Futures Exchange (SFE), both within and out of sample. Half-hourly observations are sampled from transaction data for the share price index (SPI) futures, SPI futures options, and 90-day bank accepted bill (BAB) futures markets, and the analysis is carried out using the simultaneous volatility (SVL) system of equations as well as competing volatility models. The results confirm the poor ability of GARCH models to fit intraday data. This study also applies an artificial nesting procedure to evaluate the out-of-sample volatility forecasts. Implied volatility has very limited (if any) predictive power when evaluated in isolation, whereas the SVL model with implied volatility embedded provides incremental information relative to competing model forecasts.