Examining the Return–Volatility Relation for Foreign Exchange: Evidence from the Euro VIX

We compare the return–volatility relation for the euro currency to the equivalent relation for the equity market, examining the sign, symmetry, and strength of the relation. We employ the euro‐currency exchange‐traded fund (FXE) and its associated option implied volatility index (the EVZ), whereas previous studies only employ equities and/or realized volatility. The equity studies find a negative asymmetric return–volatility relation for implied volatility, with a strong relation when large market movements occur. We find that the euro return–volatility relation can possess either a positive or negative sign, is asymmetric, and has a weaker relation. Thus, the sign and strength of the euro relation differs from the equivalent equity relation. Our quantile regressions show that both the positive and negative contemporaneous returns of the euro result in increased volatility in the extreme quantiles of the conditional distribution, with the contemporaneous effect showing a stronger relation when the euro depreciates. We also find that the volume of the euro‐currency ETF options affects the return–volatility relation for the euro ETF. Overall, the results here expand the concept originally restricted to equities, with the surprising results that the return‐implied volatility relation is weaker and the asymmetric return sometimes is positive for the euro currency. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:74–92, 2014     

Smiling less at LIFFE

This study investigates the structure of the implied volatility smile, using the prices of equity options traded on the LIFFE. First, the slope of the implied volatility curve is significantly negative for both individual stocks and index options, and the slope is less negative for longer‐term options. The implied volatility skew can be described by risk‐neutral skewness and kurtosis, with the former having the first‐order effect. Moreover, the implied volatility skew for individual stock options is less severe than for index options. Finally, the relationship between the real and risk‐neutral moments implied in option prices is significant. The results indicate that, for equity options traded on the LIFFE, the slope of the implied volatility skew is flatter than that on the Chicago Board of Exchange (CBOE). © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:57–81, 2008     

Informed options trading on the implied volatility surface: A cross-sectional approach

This study investigates the cross-sectional implication of informed options trading across different strikes and maturities. We explore the term structure perspective of the one-way information transmission from options markets to stock markets by adopting well-known option-implied volatility measures to examine stock return predictability. Using equity options data for U.S. listed stocks spanning 2000–2013, we find that the shape of the long-term implied volatility curve exhibits extra predictive power for stock returns of subsequent months even after orthogonalizing the short-term components. Our findings indicate that the inter-market information asymmetry rapidly disappears before the expiration of long-term option contracts.     

Does global fear predict fear in BRICS stock markets? Evidence from a Bayesian Graphical Structural VAR model

We examine the predictive power of implied volatility in the commodity and major developed stock markets for the implied volatility in individual BRICS stock markets. We use daily data from March 2011 to October 2016 and employ the newly developed Bayesian Graphical Structural Vector Autoregressive (BGSVAR) model of Ahelegbey et al. (2016). Evidence suggests that the predictability of individual implied volatilities in BRICS is generally a function of both global and within the group stock market implied volatilities, and that the role of commodity market volatility is marginal, except for South Africa. Important implications for policy-makers and portfolio-managers are discussed.     

Stock return dynamics,option volume,and the information content of implied volatility

This article reports new empirical results on the information content of implied volatility, with respect to modeling and forecasting the volatility of individual firm returns. The 50 firms with the highest option volume on the Chicago Board Options Exchange between 1988 and 1995 are examined. First, the results indicate that the ability of implied volatility to subsume all relevant information about conditional variance depends on option trading volume. For the most active options in the sample, implied volatility reliably outperforms GARCH and subsumes all information in return shocks beyond the first lag. For these active options, implied volatility performs substantially better than indicated by the prior results of Lamoureux and Lastrapes ( 1993 ), despite significant methodological improvements in the time‐series volatility models in this study including the use of high‐frequency intraday return shocks. For the lower option‐volume firms in the sample, the performance of implied volatility deteriorates relative to time‐series volatility models. Finally, compared to a time‐series approach, the implied volatility of equity index options provides reliable incremental information about future firm‐level volatility. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:615–646, 2003     

Regime‐switching in stock index and Treasury futures returns and measures of stock market stress

We investigate bivariate regime‐switching in daily futures‐contract returns for the US stock index and ten‐year Treasury notes over the crisis‐rich 1997–2005 period. We allow the return means, volatilities, and correlation to all vary across regimes. We document a striking contrast between regimes, with a high‐stress regime that exhibits a much higher stock volatility, a much lower stock–bond correlation, and a higher mean bond return. The high‐stress regime is associated with higher average values of stock‐implied volatility, stock illiquidity, and stock and bond futures trading volume. The lagged implied volatility from equity‐index options is useful in modeling the time‐varying transition probabilities of the regime‐switching process. Our findings support the notions that: (1) stock market stress can have a material influence on Treasury bond pricing, and (2) the diversification benefits of combined stock–bond holdings tend to be greater during times with relatively high stock market stress. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:753–779, 2010     

The impact of net buying pressure on index options prices

This study examines whether the demand for options, as measured by the net buying pressure of index options, explains the implied volatility structure created by options prices. We decompose the buying pressure into the direction‐motivated (i.e., delta‐informed) and the volatility‐motivated (i.e., vega‐informed) demand for options. After controlling for options traders' hedging demand, we find that both delta‐ and vega‐informed trading play significant roles in explaining changes in implied volatility. Foreign institutions are more directionally informed in index options trading than their domestic counterparts are. Domestic investors effectively implement volatility trading using put options.     

The interrelation of price volatility and trading volume of currency options

This article examines the interrelations between future volatility of the U.S. dollar/British pound exchange rate and trading volume of currency options for the British pound. The future volatility of the exchange rate is approximated alternatively by implied volatility and by IGARCH volatility. The results suggest the presence of strong contemporaneous positive feedbacks between the exchange rate volatility and the trading volume of call and put options. Previous option volumes have significant predictive power with respect to the expected future volatility of the dollar/pound exchange rate. Similarly, lagged volatilities jointly have significant predictive power for option volume. Although option volume (volatility) responds somewhat differently to individual volatility (volume) terms under the two volatility measures, the overall volume‐volatility relations are broadly similar between the implied and IGARCH volatilities. The results generally support the hypothesis that the information‐based trading explains more of the trading volume in currency options on the U.S. dollar/British pound exchange rate than hedging. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:681–700, 2003     

The impact of net buying pressure on VIX option prices

This paper analyzes the impact of intraday trading activity on option prices in the Volatility Index (VIX) options market. Our results show that there is a temporal relationship between net buying pressure (NBP) and changes in implied volatility of VIX options. Moreover, an increase in NBPs lowers the next-day delta-hedged option returns. Using several measures proxying for limits to arbitrage, the average levels of the implied volatility curve rise when limits to arbitrage are severe. A trading strategy in the VIX futures market constructed by using the NBP generates an average annualized return of 10.09%.     

Quantile Regression Analysis of the Asymmetric Return‐Volatility Relation

We use quantile regression to investigate the short‐term return‐volatility relation between stock index returns and changes in implied volatility index. Neither the leverage hypothesis nor the volatility feedback hypothesis effectively explains the asymmetric return‐volatility relation. Instead, behavioral explanations, such as the affect and representativeness heuristics, are supported by our results, particularly in the short‐term; the affect heuristic plays an important role. Moreover, in the context of an extreme volatility change distribution, the affect heuristic and time‐pressure dominate. Thus, we observe strong negative and asymmetric relations between each volatility index and its corresponding stock market index. The asymmetry increases monotonically from the median quantile to the uppermost quantile (i.e., 95%); therefore, ordinary least squares (OLS) regression underestimates this relation at upper quantiles. Additionally, the VIX presents the highest asymmetric return‐volatility relation, followed by the VSTOXX, VDAX, and VXN. Finally, the observed asymmetry is more pronounced with the new volatility index measure than with the old, at‐the‐money volatility index measure. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:235–265, 2013     

FROM SMILE ASYMPTOTICS TO MARKET RISK MEASURES

The left tail of the implied volatility skew, coming from quotes on out‐of‐the‐money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be integrated into the theoretical framework of convex monetary measures of risk. In particular, we make use of indifference pricing by dynamic convex risk measures, which are given as solutions of backward stochastic differential equations, to establish a link between these two approaches to risk measurement. We derive a characterization of the implied volatility in terms of the solution of a nonlinear partial differential equation and provide a small time‐to‐maturity expansion and numerical solutions. This procedure allows to choose convex risk measures in a conveniently parameterized class, distorted entropic dynamic risk measures, which we introduce here, such that the asymptotic volatility skew under indifference pricing can be matched with the market skew. We demonstrate this in a calibration exercise to market implied volatility data.     

Show me the money: Option moneyness concentration and future stock returns

Informed traders often use options that are not in-the-money due to higher potential gains for a smaller upfront cost. Thus, trading activity by option moneyness should be a gauge of informed option trading. We construct a dollar volume-weighted average moneyness measure to capture option trading activity at different moneyness levels. Stock returns increase with this measure, suggesting more trading activity in options with higher leverage predicts future stock returns. Our results hold cross-sectionally and at the portfolio level yielding a Fama–French five-factor α of 12% per year for all stocks and 33% per year for high implied volatility stocks.     

Cross-dynamics of volatility term structures implied by foreign exchange options

This paper examines the cross-dynamics of volatility term structure slopes implied by foreign exchange options. The empirical findings demonstrate that a few principal components can explain a vast proportion of the variation in volatility term structure slopes across the major exchange rates. Furthermore, the results indicate that the euro is the dominant currency, as the implied volatility term structure of the euro is found to affect all the other volatility term structures, while the term structure of the euro appears to be virtually unaffected by the other currencies. Finally, our results provide evidence of significant nonlinearities in the relationship between the euro and the Swiss franc.     

Option‐Expiration Effects in Small Markets: The Spanish Stock Exchange

This study analyzes the effect of the expiration of the Ibex‐35 Index derivatives, as well as the first four stock options traded in the Spanish Equity Derivatives Exchange, on the return, conditional volatility, and trading volume of the underlying assets. The analysis covers the period from the introduction of the various derivatives to December 1995. This period has been divided into two subperiods in order to determine if there are changes in the conclusions. The expiration of the Ibex‐35 index derivatives is associated with an increase in the trading volume of the underlying asset, but it has no significant effect on either the underlying asset prices or on the level of volatility on the expiration day. However, the expiration of the stock options has significant impact on their underlying assets. We observed a downward pressure on prices and a reduction of volatility level in the week before the expiration date and a significant increase in trading volume on the expiration day. The absence of futures contracts on individual stocks, among other possible causes, may explain these differences. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:905–928, 2001     

Valuing real options using implied binomial trees and commodity futures options

A real option on a commodity is valued using an implied binomial tree (IBT) calibrated using commodity futures options prices. Estimating an IBT in the absence of spot options (the norm for commodities) allows real option models to be calibrated for the first time to market‐implied probability distributions for commodity prices. In addition, the existence of long‐dated futures options means that good volatility estimates may now be incorporated into capital budgeting evaluations of real options projects with long planning horizons. An example is given using gold futures options and a real option to extract gold from a mine. A detailed out‐of‐sample test is included that shows how IBT option pricing errors evolve on subtrees emanating from future levels of the underlying asset. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:203–226, 2007     

PRICING EQUITY DERIVATIVES SUBJECT TO BANKRUPTCY

We solve in closed form a parsimonious extension of the Black–Scholes–Merton model with bankruptcy where the hazard rate of bankruptcy is a negative power of the stock price. Combining a scale change and a measure change, the model dynamics is reduced to a linear stochastic differential equation whose solution is a diffusion process that plays a central role in the pricing of Asian options. The solution is in the form of a spectral expansion associated with the diffusion infinitesimal generator. The latter is closely related to the Schrödinger operator with Morse potential. Pricing formulas for both corporate bonds and stock options are obtained in closed form. Term credit spreads on corporate bonds and implied volatility skews of stock options are closely linked in this model, with parameters of the hazard rate specification controlling both the shape of the term structure of credit spreads and the slope of the implied volatility skew. Our analytical formulas are easy to implement and should prove useful to researchers and practitioners in corporate debt and equity derivatives markets.     

Implied volatility forecasts in the grains complex

This article finds that the implied volatilities of corn, soybean, and wheat futures options 4 weeks before option expiration have significant predictive power for the underlying futures contract return volatilities through option expiration from January 1988 through September 1999. These implied volatilities also encompass the information in out‐of‐sample seasonal Glosten, Jagannathan, and Runkle (GJR;1993) volatility forecasts. Evidence also demonstrates that when corn‐implied volatility rises relative to out‐of‐sample seasonal GJR volatility forecasts, implied volatility substantially overpredicts realized volatility. However, simulations of trading rules that involve selling corn option straddles when corn‐implied volatility is high relative to out‐of‐sample GJR volatility forecasts indicate that none of the trading rules would have been significantly profitable. This finding suggests that these options are not necessarily overpriced. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:959–981, 2002     

基于高频数据的波动率与成交量动态关系研究

传统的价量分析都是从低频数据来分析股票市场上波动率、收益率与成交量之间的关系。基于高频数据,利用分位数回归并结合高频数据的波动率估计方法对高频数据中所呈现出的价量关系进行研究,并分析了股票价格跳跃过程所带来的跳跃方差与成交量之间的关系。实证分析表明：指数及个股收益率与成交量之间的关系并不显著;波动率、跳跃与成交量之间存在着显著相关的关系,个股的波动率与成交量之间的关系显著并呈现出正向相关关系,而指数的波动率与成交量之间呈现出一种负向关系,并且关系比较微弱;个股的成交量的改变会导致股票价格的跳跃方差的减小,而指数的成交量的改变则使得指数的跳跃方差增大。     

Bid and ask prices of index put options: Which predicts the underlying stock returns?

In this study, we separately estimate the implied volatility from the bid and ask prices of deep out-of-the-money put options on the S&P500 index. We find that the implied volatility of ask prices has stronger predictive power for stock returns than does the implied volatility of bid prices. We identify two sources of the better performance of the ask price implied volatility: one is its stronger predictive power during economic recessions and in the presence of increasing intermediary capital risk, and the other is its richer information about the future market variance risk premium.     

Properties and the predictive power of implied volatility in the New Zealand dairy market

This study develops a dairy implied volatility index (DVIX), derived from New Zealand Exchange traded options on whole milk powder (WMP) futures. We document an inverse return–volatility relation which is asymmetric, where increases in WMP futures prices are associated with larger absolute changes in the DVIX than decreases. In sample, the results strongly suggest that the DVIX has a high information content regarding conditional variance and that the inclusion of historical information further improves the predictive power. Out of sample, we find that the DVIX provides substantial information about future realized volatility. We also document that a combination of historical volatility and the DVIX provides the best out-of-sample forecasts.