The forecast quality of CBOE implied volatility indexes

We examine the forecast quality of Chicago Board Options Exchange (CBOE) implied volatility indexes based on the Nasdaq 100 and Standard and Poor's 100 and 500 stock indexes. We find that the forecast quality of CBOE implied volatilities for the S&P 100 (VXO) and S&P 500 (VIX) has improved since 1995. Implied volatilities for the Nasdaq 100 (VXN) appear to provide even higher quality forecasts of future volatility. We further find that attenuation biases induced by the econometric problem of errors in variables appear to have largely disappeared from CBOE volatility index data since 1995. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:339–373, 2005     

Information content of volatility spreads

This study reexamines the determinants of volatility spreads and suggests a new forecast of future volatilities. Contrary to earlier volatility forecasts, the newly introduced forecast is applicable when investors are not risk‐neutral or when underlying returns do not follow a Gaussian probability distribution. This implies that the method is consistent with the presence of risk premia for other risks such as volatility risk. Using S&P 500 index options, we show that the new volatility forecast outperforms other volatility forecasts including risk‐neutral implied volatility and historical volatility in two aspects. First, the new forecast is superior to other estimates in terms of forecasting errors for future realized volatilities. Second, it is an unbiased estimator of future realized volatilities. This is shown using an encompassing regression analysis. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:533–558, 2010     

Is there information in the volatility skew?

Since the 1987 crash, option prices have exhibited a strong negative skew, implying higher implied volatility for out‐of‐the‐money puts than at‐ and in‐the‐money puts. This has resulted in incorporating multiple jumps and stochastic volatility within the data generating process to improve the Black–Scholes model in an attempt to capture negative skewness and a highly leptokurtic distribution. The general conclusion is that there is a large jump premium in the short term, which best explains the significant negative skew for short maturity options. Alternative explanations for the negative skew are related to market liquidity driven by demand shocks and supply shortages. Regardless of the explanation for the negative skew, we assess the information content in the shape of the skew to infer if the option market can accurately forecast stock market crashes and/or spikes upward. We demonstrate, using all options on the S&P 100 from 1984–2006, that the shape of the skew can reveal with significant probability when the market will crash or spike. However, we find the magnitude of the spike prediction is not economically significant. Our findings are strongest for the short‐term out‐of‐the money puts, consistent with the notion of investors' aversion to large negative movements. We also find that the power of the crash/spike prediction decreases with an increase in the time to option maturity. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:921–959, 2007     

Testing range estimators of historical volatility

This study investigates the relative performance of various historical volatility estimators that incorporate daily trading range: M. Parkinson (1980), M. Garman and M. Klass (1980), L. C. G. Rogers and S. E. Satchell (1991), and D. Yang and Q. Zhang (2000). It is found that the range estimators all perform very well when an asset price follows a continuous geometric Brownian motion. However, significant differences among various range estimators are detected if the asset return distribution involves an opening jump or a large drift. By adding microstructure noise to the Monte Carlo simulation, the finding of S. Alizadeh, M. W. Brandt, and F. X. Diebold (2002)—that range estimators are fairly robust toward microstructure effects—is confirmed. An empirical test with S&P 500 index return data shows that the variances estimated with range estimators are quite close to the daily integrated variance. The empirical results support the use of range estimators for actual market data. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:297–313, 2006     

The implied volatility smirk of commodity options

This paper studies the implied volatility (IV) smirks in four commodity markets by adopting Zhang and Xiang's methodology. First, we document the term structure and dynamics of IV smirks. Overall, the commodity IV curves are negatively skewed with a positive curvature. Then we analyze the commodity and S&P 500 returns' predictability based on in‐sample and out‐of‐sample tests and find that the information embedded in IV smirks can significantly predict monthly commodity and S&P 500 returns. For example, the risk‐neutral fourth cumulant (FC) from the crude oil market outperforms all of the standard predictors in predicting the S&P 500 returns.     

Factors explaining movements in the implied volatility surface

This article explores the relationship of changes in the S&P 500 index implied volatility surface to economic state variables. Observable variables can explain some of the variation in implied volatility, with the majority of explanatory power from index returns. Although the contemporaneous return is most important for explaining changes in short dated volatility, the path of the index is important for explaining changes in long dated volatility. Other variables also display statistically significant relations to volatility changes. Shocks to the Nikkei 225, short‐term interest rates, and the corporate/government bond yield spread are correlated with small, systematic changes in implied volatility. The results suggest a multifactor model for market volatility, with factors other than index returns adding negligible explanatory ability. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:915–937, 2002     

Predicting financial volatility: High‐frequency time‐series forecasts vis‐à‐vis implied volatility

Recent evidence suggests option implied volatilities provide better forecasts of financial volatility than time‐series models based on historical daily returns. In this study both the measurement and the forecasting of financial volatility is improved using high‐frequency data and long memory modeling, the latest proposed method to model volatility. This is the first study to extract results for three separate asset classes, equity, foreign exchange, and commodities. The results for the S&P 500, YEN/USD, and Light, Sweet Crude Oil provide a robust indication that volatility forecasts based on historical intraday returns do provide good volatility forecasts that can compete with and even outperform implied volatility. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:1005–1028, 2004     

The impact of volatility derivatives on S&P500 volatility

This study investigates whether the newly cultivated platform of volatility derivatives has altered the volatility of the underlying S&P500 index. The findings suggest that the onset of the volatility derivatives trading has lowered the volatility of both the cash market volatility and the cash market index, and significantly reduced the impact of shocks to volatility. When big sudden events hit financial markets, however, the volatility of volatility seems to elevate in the U.S. equity market as a result of increased global correlations. Regardless of the period under examination and the estimator employed, long‐run volatility persistence is present. The latter drops significantly when the credit crunch period is excluded from the post‐event date sample period. The correlation between the broad equity index and the return volatility remains low, which in turn strengthens the role of volatility derivatives to facilitate portfolio diversification. The analysis also shows that volatility is mean reverting, whereas market data support the impact of information asymmetries on conditional volatility. In the post‐event date phase, no asymmetries are found when the recent crisis is not accounted for. Finally, comparisons with other international equity indices, with no volatility derivatives listed, unveil that these indices exhibit higher volatility and slower recovery from shocks than the S&P500 index. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:1190–1213, 2009     

The information content of implied volatility: Evidence from Australia

This study develops an implied volatility index for the Australian stock market, termed as the AVX, and assesses its information content. The AVX is constructed using S&P/ASX 200 index options with a constant time‐to‐maturity of three months. It is observed that the AVX has a significant negative and asymmetric relationship with S&P/ASX 200 returns. When evaluating the forecasting power of the AVX for future stock market volatility, it is found that the AVX contains important information both in‐sample and out‐of‐sample. In‐sample, the AVX significantly improves the fit of a GJR‐GARCH(1, 1) model. Out‐of‐sample, the AVX significantly outperforms the RiskMetrics approach and the GJR‐GARCH(1, 1) model, with its highest forecasting power at the one‐month forecasting horizon. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:134–155, 2010     

The Fed's policy decisions and implied volatility

This study examines how the Fed's monetary policy decisions affect the implied volatility of the S&P 500 index. The results show that stock market uncertainty is significantly affected by the Fed's policy decisions. In particular, we find that implied volatility generally decreases after FOMC meetings, while the relationship between target rate surprises and market uncertainty appears positive. However, our results also suggest that the apparent positive relationship between policy surprises and implied volatility is mostly driven by the volatility‐reducing effects of negative surprises. We further document that implied volatility is affected by both scheduled and unscheduled policy actions, with the scheduled path surprises having the strongest impact on volatility. Finally, our findings indicate that the impact of monetary policy decisions on implied volatility is more pronounced during periods of expansive policy. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark     

Market volatility and the demand for hedging in stock index futures

This study examines the relation between stock market volatility and the demand for hedging in S&P 500 stock index futures contracts. Open interest is used as a proxy for hedging demand. The analysis employs unique data that identify separately the open interest of large hedgers, large speculators, and smaller traders. Volatility estimates are decomposed into expected and unexpected components, to assess whether traders’ reactions to volatility depend upon its predictability. Results indicate that daily open interest for hedgers increases when unexpected volatility increases. Increases in unexpected volatility may cause hedgers to raise their estimates of future expected volatility, and hence increase their demand for hedging. Open interest of speculators is not related to expected volatility, and is only weakly related to unexpected volatility. The increase in the participation of hedgers in periods of higher volatility is significantly larger than the increase in the participation of speculators. The results suggest that increases in stock market volatility increase the demand for hedging. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 105–125, 2000     

The information content of the S&P 500 index and VIX options on the dynamics of the S&P 500 index

Given that both S&P 500 index and VIX options essentially contain information about the future dynamics of the S&P 500 index, in this study, we set out to empirically investigate the informational roles played by these two option markets with regard to the prediction of returns, volatility, and density in the S&P 500 index. Our results reveal that the information content implied from these two option markets is not identical. In addition to the information extracted from the S&P 500 index options, all of the predictions for the S&P 500 index are significantly improved by the information recovered from the VIX options. Our findings are robust to various measures of realized volatility and methods of density evaluation. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Asymmetric pricing of implied systematic volatility in the cross‐section of expected returns

Assuming a symmetric relation between returns and innovations in implied market volatility, Ang, A., Hodrick, R., Xing, Y., and Zhang, X. (2006) find that sensitivities to changes in implied market volatility have a cross‐sectional effect on firm returns. Dennis, P., Mayhew, S., and Stivers, C. (2006), however, find an asymmetric relation between firm‐level returns and implied market volatility innovations. We incorporate this asymmetry into the cross‐sectional relation between sensitivity to volatility innovations and returns. Using both portfolio sorting and firm‐level regressions, we find that sensitivity to VIX innovations is negatively related to returns when volatility is rising, but is unrelated when it is falling. The negative relation is robust to controls for other variables, suggesting only the increase in implied market volatility is a priced risk factor. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:34–54, 2011     

Local volatility under rough volatility

Several asymptotic results for the implied volatility generated by a rough volatility model have been obtained in recent years (notably in the small-maturity regime), providing a better understanding of the shapes of the volatility surface induced by rough volatility models, supporting their calibration power to SP500 option data. Rough volatility models also generate a local volatility surface, via the so-called Markovian projection of the stochastic volatility. We complement the existing results on implied volatility by studying the asymptotic behavior of the local volatility surface generated by a class of rough stochastic volatility models, encompassing the rough Bergomi model. Notably, we observe that the celebrated “1/2 skew rule” linking the short-term at-the-money skew of the implied volatility to the short-term at-the-money skew of the local volatility, a consequence of the celebrated “harmonic mean formula” of [Berestycki et al. (2002). Quantitative Finance, 2, 61–69], is replaced by a new rule: the ratio of the at-the-money implied and local volatility skews tends to the constant $1/(H+3/2)$ (as opposed to the constant 1/2), where H is the regularity index of the underlying instantaneous volatility process.     

EQUILIBRIUM ASSET AND OPTION PRICING UNDER JUMP DIFFUSION

This paper develops an equilibrium asset and option pricing model in a production economy under jump diffusion. The model provides analytical formulas for an equity premium and a more general pricing kernel that links the physical and risk‐neutral densities. The model explains the two empirical phenomena of the negative variance risk premium and implied volatility smirk if market crashes are expected. Model estimation with the S&P 500 index from 1985 to 2005 shows that jump size is indeed negative and the risk aversion coefficient has a reasonable value when taking the jump into account.     

Exchange Traded Funds and Stock Market Volatility

This study investigates the relationship between the volatility of stock market indexes and the trading volumes of their exchange traded funds (ETFs). Using both ordinary least squares and generalized autoregressive conditional heteroskedasticity approaches, we demonstrate that the contemporaneous trading volume of S&P 500 ETFs is a key determinant of S&P 500 volatility at both monthly and daily frequencies. Vector autoregressive estimation on the other hand suggests a two‐way Granger causality between S&P 500 volatility and the trading of S&P 500 ETFs. A replication analysis of other market indexes and the corresponding ETFs tracking these indexes confirms that these findings are robust.     

The information content of option implied volatility surrounding the 1997 Hong Kong stock market crash

This study examines the information conveyed by options and examines their implied volatility at the time of the 1997 Hong Kong stock market crash. The author determines the efficiency of implied volatility as a predictor of future volatility by comparing it to other leading indicator candidates. These include volume and open interest of index options and futures, as well as the arbitrage basis of index futures. Using monthly, nonoverlapping data, the study reveals that implied volatility is superior to those variables in forecasting future realized volatility. The study also demonstrates that a simple signal extraction model could have produced useful warning signals prior to periods of extreme volatility. These results indicate that the options market is highly efficient informationally. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:555–574, 2007     

New evidence on expiration‐day effects using realized volatility: An intraday analysis for the Spanish stock exchange

Additional evidence is provided on expiration effects in the Ibex 35 stock index futures market using realized volatility as proposed by T. G. Andersen, T. Bollerslev, F. X. Diebold, and P. Labys (2003). Findings reveal not only a significant increase in spot trading activity, but also the existence of a significant jump in spot volatility at index futures expiration. Moreover, the importance of the data frequency considered is analyzed. Our research reveals that the use of GARCH methodology from daily data does not have the ability to statistically assess such expiration‐day effect. Additional empirical evidence is provided for the S&P 500 stock index futures market. Neither unconditional nor conditional realized volatility has a significant increase at expiration for the U.S. market, suggesting that this effect is specific for the Spanish market, at least for the period analyzed. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:923–938, 2006     

Equity volatility,bond yields,and yield spreads

This study examines the impact of implied and contemporaneous equity market volatility on Treasury yields, corporate bond yields, and yield spreads over Treasuries. The CBOE VIX is the measure of implied volatility, and the measure of contemporaneous volatility is constructed using intraday squared S&P 500 returns. We find that bond yields and spreads respond to changes in equity market volatility in a manner consistent with a flight‐to‐quality effect. Both short‐ and long‐term Treasury yields fall in response to increases in implied volatility, and the yield curve flattens modestly. Yields on short‐term investment grade bonds fall in response to contemporaneous volatility shocks, while long‐term spreads on low‐quality issues widen. This indicates that investors “look ahead” in anticipation of changes in equity market volatility but respond more strongly to changes in contemporaneous market activity. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

The information content of implied volatility in agricultural commodity markets

In this article we compare the incremental information content of lagged implied volatility to GARCH models of conditional volatility for a collection of agricultural commodities traded on the New York Board of Trade. We also assess the relevance of the additional information provided by the implied volatility in a risk management framework. It is first shown that past squared returns only marginally improve the information content provided by the lagged implied volatility. Secondly, value‐at‐risk (VaR) models that rely exclusively on lagged implied volatility perform as well as VaR models where the conditional variance is modelled according to GARCH type processes. These results indicate that the implied volatility for options on futures contracts in agricultural commodity markets provides relevant volatility information that can be used as an input to VaR models. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:441–454, 2003