When Uncertainty Blows in the Orchard: Comovement and Equilibrium Volatility Risk Premia

We provide novel evidence for an equilibrium link between investors' disagreement, the market price of volatility and correlation, and the differential pricing of index and individual equity options. We show that belief disagreement is positively related to (i) the wedge between index and individual volatility risk premia, (ii) the different slope of the smile of index and individual options, and (iii) the correlation risk premium. Priced disagreement risk also explains returns of option volatility and correlation trading strategies in a way that is robust to the inclusion of other risk factors and different market conditions.     

Trading activity and bid–ask spreads of individual equity options

We empirically examine the impact of trading activities on the liquidity of individual equity options measured by the proportional bid–ask spread. There are three main findings. First, the option return volatility, defined as the option price elasticity times the stock return volatility, has a much higher power in explaining the spread variations than the commonly considered liquidity determinants such as the stock return volatility and option trading volume. Second, after controlling for all the liquidity determinants, we find a maturity-substitution effect due to expiration cycles. When medium-term options (60–90 days maturity) are not available, traders use short-term options as substitutes whose higher volume leads to a smaller bid–ask spread or better liquidity. Third, we also find a moneyness-substitution effect induced by the stock return volatility. When the stock return volatility goes up, trading shifts from in-the-money options to out-of-the-money options, causing the latter’s spread to narrow.     

The intraday behaviors and relationships with its underlying assets: evidence on option market in Taiwan

In this paper, we use daily data to investigate the information asymmetric effects and the relationships between the trading volume of options and their underlying spot trading volume. Our results reveal that options with higher liquidity are near-the-money and expiration periods with 2 to 4 weeks have higher trading activity. We classify them into two parts with the ARIMA model: the expected trading activity impact and the unexpected trading activity impact. Using the bivariate generalized autoregressive conditional heteroscedasticity (GARCH) model, we investigate the trading activity effect and information asymmetric effect. In conclusion, the trading volume volatility of the spot and options markets move together, and a greater expected and unexpected trading volume volatility of the spot (options) market is associated with greater volatility in the options (spot) market. However, both markets generate higher trading volume volatility when people expect such an impact rather than when they do not. We also find that there are feedback effects within these two markets. Furthermore, when the spot (options) market has negative innovations, it generates a greater impact on the options (spot) market than do positive innovations. Finally, the conditional correlation coefficient between the spot and the option markets changes over time based on the bivariate GARCH model.     

Is there price discovery in equity options?

We use tick-by-tick quote data for 39 liquid US stocks and options on them, and we focus on events when the two markets disagree about the stock price in the sense that the option-implied stock price obtained from the put-call parity relation is inconsistent with the actual stock price. Option market quotes adjust to eliminate the disagreement, while the stock market quotes behave normally, as if there were no disagreement. The disagreement events are typically precipitated by stock price movements and display signed option volume in the direction that tends to eliminate the disagreements. These results show that option price quotes do not contain economically significant information about future stock prices beyond what is already reflected in current stock prices, i.e., no economically significant price discovery occurs in the option market. We also find no option market price discovery using a much larger sample of disagreement events based on a weaker definition of a disagreement, which verifies that the findings for the primary sample are not due to unusual or unrepresentative market behavior during the put-call parity violations.     

Disagreement and asset prices

How do differences of opinion affect asset prices? Do investors earn a risk premium when disagreement arises in the market? Despite their fundamental importance, these questions are among the most controversial issues in finance. In this paper, we use a novel data set that allows us to directly measure the level of disagreement among Wall Street mortgage dealers about prepayment speeds. We examine how disagreement evolves over time and study its effects on expected returns, return volatility, and trading volume in the mortgage-backed security market. We find that increased disagreement is associated with higher expected returns, higher return volatility, and larger trading volume. These results imply that there is a positive risk premium for disagreement in asset prices. We also show that volatility in and of itself does not lead to higher trading volume. Instead, only when disagreement arises in the market is higher uncertainty associated with more trading. Finally, we are able to distinguish empirically between two competing hypotheses regarding how information in markets gets incorporated into asset prices. We find that sophisticated investors appear to update their beliefs through a rational expectations mechanism when disagreement arises.     

How Do Exchanges Select Stocks for Option Listing?

We investigate the factors influencing the selection of stocks for option listing. Exchanges tend to list options on stocks with high trading volume, volatility, and market capitalization, but the relative effect of these factors has changed over time as markets have evolved. We observe a shift from volume toward volatility after the moratorium on new listings ended in 1980. Using control sample methodology designed to correct for the endogeneity of option listing, we find no evidence that volatility declines with option introduction, in contrast to previous studies that do not use control samples.     

Volatility Information Trading in the Option Market

This paper investigates informed trading on stock volatility in the option market. We construct non-market maker net demand for volatility from the trading volume of individual equity options and find that this demand is informative about the future realized volatility of underlying stocks. We also find that the impact of volatility demand on option prices is positive. More importantly, the price impact increases by 40% as informational asymmetry about stock volatility intensifies in the days leading up to earnings announcements and diminishes to its normal level soon after the volatility uncertainty is resolved.     

How Do Quasi‐Random Option Grants Affect CEO Risk‐Taking?

We examine how an increase in stock option grants affects CEO risk‐taking. The overall net effect of option grants is theoretically ambiguous for risk‐averse CEOs. To overcome the endogeneity of option grants, we exploit institutional features of multiyear compensation plans, which generate two distinct types of variation in the timing of when large increases in new at‐the‐money options are granted. We find that, given average grant levels during our sample period, a 10% increase in new options granted leads to a 2.8% to 4.2% increase in equity volatility. This increase in risk is driven largely by increased leverage.     

Can we forecast the implied volatility surface dynamics of equity options? Predictability and economic value tests

We examine whether the dynamics of the implied volatility surface of individual equity options contains exploitable predictability patterns. Predictability in implied volatilities is expected due to the learning behavior of agents in option markets. In particular, we explore the possibility that the dynamics of the implied volatility surface of individual stocks may be associated with movements in the volatility surface of S&P 500 index options. We present evidence of strong predictable features in the cross-section of equity options and of dynamic linkages between the volatility surfaces of equity and S&P 500 index options. Moreover, time-variation in stock option volatility surfaces is best predicted by incorporating information from the dynamics in the surface of S&P 500 options. We analyze the economic value of such dynamic patterns using strategies that trade straddle and delta-hedged portfolios, and find that before transaction costs such strategies produce abnormal risk-adjusted returns.     

Overconfidence among option traders

The investor overconfidence theory predicts a direct relationship between market‐wide turnover and lagged market return. However, previous research has examined this prediction in the equity market, we focus on trading in the options market. Controlling for stock market cross‐sectional volatility, stock idiosyncratic risk, and option market volatility, we find that option trading turnover is positively related to past stock market return. In addition, call option turnover and call to put ratio are also positively associated with the past stock market return. These findings are consistent with the overconfidence theory. We also find that overconfident investors trade more in the options market than in the equity market. We rule out explanations other than investor overconfidence, such as momentum trading and varying risk preferences, for our findings.     

Equity‐Based Incentives,Risk Aversion,and Merger‐Related Risk‐Taking Behavior

We find that post‐merger equity risk is negatively related to the sensitivity of CEO wealth to stock return volatility (vega), but is concentrated in CEOs with high proportions of options and options that are more in‐the‐money. The probability of industrial diversification also increases in vega. Additional tests show that the decline in post‐merger equity risk results in a significant decrease in shareholder wealth. This decrease is concentrated among firms with CEOs having the highest delta and the highest delta and vega. Our results suggest that the increased convexity provided by option‐based compensation does not necessarily increase risk‐taking behavior by CEOs.     

Disagreement and Learning: Dynamic Patterns of Trade

The empirical evidence on investor disagreement and trading volume is difficult to reconcile in standard rational expectations models. We develop a dynamic model in which investors disagree about the interpretation of public information. We obtain a closed‐form linear equilibrium that allows us to study which restrictions on the disagreement process yield empirically observed volume and return dynamics. We show that when investors have infrequent but major disagreements, there is positive autocorrelation in volume and positive correlation between volume and volatility. We also derive novel empirical predictions that relate the degree and frequency of disagreement to volume and volatility dynamics.     

Options and earnings announcements: an empirical study of volatility, trading volume, open interest and liquidity

In this paper we study the impact of earnings announcements on implied volatility, trading volume, open interest and spreads in the stock options market. We find that implied volatility increases before announcement days and drops afterwards. Also option trading volume is higher around announcement days. During the days before the announcement open interest tends to increase, while it returns to regular levels afterwards. Changes in the quoted spread largely respond to higher trading volume and changes in implied volatility. The effective spread increases on the event day and on the first two days following the earnings announcement.     

VOLATILITY FORECASTS,TRADING VOLUME,AND THE ARCH VERSUS OPTION‐IMPLIED VOLATILITY TRADE‐OFF

We investigate empirically the role of trading volume (1) in predicting the relative informativeness of volatility forecasts produced by autoregressive conditional heteroskedasticity (ARCH) models versus the volatility forecasts derived from option prices, and (2) in improving volatility forecasts produced by ARCH and option models and combinations of models. Daily and monthly data are explored. We find that if trading volume was low during period t?1 relative to the recent past, ARCH is at least as important as options for forecasting future stock market volatility. Conversely, if volume was high during period t?1 relative to the recent past, option‐implied volatility is much more important than ARCH for forecasting future volatility. Considering relative trading volume as a proxy for changes in the set of information available to investors, our findings reveal an important switching role for trading volume between a volatility forecast that reflects relatively stale information (the historical ARCH estimate) and the option‐implied forward‐looking estimate.     

THE ECONOMIC VALUE OF USING REALIZED VOLATILITY IN FORECASTING FUTURE IMPLIED VOLATILITY

We examine the economic benefits of using realized volatility to forecast future implied volatility for pricing, trading, and hedging in the S&P 500 index options market. We propose an encompassing regression approach to forecast future implied volatility, and hence future option prices, by combining historical realized volatility and current implied volatility. Although the use of realized volatility results in superior performance in the encompassing regressions and out-of-sample option pricing tests, we do not find any significant economic gains in option trading and hedging strategies in the presence of transaction costs.     

Option prices and stock market momentum: evidence from China

Option prices tend to be correlated to past stock market returns due to market imperfections. We unprecedentedly examine this issue on the SSE 50 ETF option in the Chinese derivatives market. To measure the price pressure in the options market, we construct an implied volatility spread based on pairs of the SSE 50 ETF option with identical expiration dates and strike prices. By regressing the implied volatility spread on past stock returns, we find that past stock returns exert a strong influence on the pricing of index options. Specifically, we find that SSE 50 ETF calls are significantly overvalued relative to SSE 50 ETF puts after stock price increases and the reverse is also true after the stock price decreases. Moreover, we validate the momentum effects in the underlying stock market to be responsible for the price pressure. These findings are both economically and statistically significant and have important implications.     

The Informational Role of Option Trading Volume in Equity Index Options Markets

This paper examines the dynamic relations between future price volatility of the S&P 500 index and trading volume of S&P 500 options to explore the informational role of option volume in predicting the price volatility. The future volatility of the index is approximated alternatively by implied volatility and by EGARCH volatility. Using a simultaneous equation model to capture the volume-volatility relations, the paper finds that strong contemporaneous feedbacks exist between the future price volatility and the trading volume of call and put options. Previous option volumes have a strong predictive ability with respect to the future price volatility. Similarly, lagged changes in volatility have a significant predictive power for option volume. Although the volume-volatility relations for individual volatility and volume terms are somewhat different under the two volatility measures, the results on the predictive ability of volume (volatility) for volatility (volume) are broadly similar between the implied and EGARCH volatilities. These findings support the hypothesis that both the information- and hedge-related trading explain most of the trading volume of equity index options.     

Model Uncertainty and Option Markets with Heterogeneous Beliefs

This paper provides option pricing and volume implications for an economy with heterogeneous agents who face model uncertainty and have different beliefs on expected returns. Market incompleteness makes options nonredundant, while heterogeneity creates a link between differences in beliefs and option volumes. We solve for both option prices and volumes and test the joint empirical implications using S&P500 index option data. Specifically, we use survey data to build an Index of Dispersion in Beliefs and find that a model that takes information heterogeneity into account can explain the dynamics of option volume and the smile better than can reduced‐form models with stochastic volatility.     

International tax arbitrage,currency options and put-call parity conditions

Using a finite-horizon general equilibrium model with uncertainty and money, we characterize situations where tax arbitrage opportunities may arise for international portfolio investors in an economy with heterogeneous capital income taxation where foreign currency exposure can be hedged using forward contracts and a set of currency options. We obtain tax-modified option prices similar to the no-tax ones, but augmented by tax-induced “risk-premium” terms; tax-modified put-call parity conditions are derived that revert to their standard (no-tax) format if the respective marginal agents in the bond and option markets are in identical tax brackets.     

Understanding Delta-Hedged Option Returns in Stochastic Volatility Environments

In this paper, we provide a novel representation of delta-hedged option returns in a stochastic volatility environment. The representation of delta-hedged option returns provided in this paper consists of two terms: volatility risk premium and parameter estimation risk. In an empirical analysis, we examine delta-hedged option returns based on the result of a historical simulation with the USD-JPY currency option market data from October 2003 to June 2010. We find that the delta-hedged option returns for OTM put options are strongly affected by parameter estimation risk as well as the volatility risk premium, especially in the post-Lehman shock period.