Implied Volatility in Options Markets and Conditional Heteroscedasticity in Stock Markets

This study examines whether or not the volatility of stock index returns forecasted by a GARCH-M specification is consistent with the implied volatility observed in options markets. Recent data for the New York Stock Exchange Composite Index and Standard & Poor's 500 Index and their options are employed. The patterns of the term structure of implied volatility are compared with those of volatility estimates obtained from the GARCH process. The results indicate that the GARCH process appears to partially explain the variation of implied volatilities and the term structure of implied volatilities.     

Estimating daily volatility in financial markets utilizing intraday data

This study proposes a new approach to the estimation of daily realised volatility in financial markets from intraday data. Initially, an examination of intraday returns on S&P 500 Index Futures reveals that returns can be characterised by heteroscedasticity and time-varying autocorrelation. After reviewing a number of daily realised volatility estimators cited in the literature, it is concluded that these estimators are based upon a number of restrictive assumptions in regard to the data generating process for intraday returns. We use a weak set of assumptions about the data generating process for intraday returns, including transaction returns, given in den Haan and Levin [den Haan, W.J., Levin, A., 1996. Inferences from parametric and non-parametric covariance matrix estimation procedures, Working paper, NBER, 195.], which allows for heteroscedasticity and time-varying autocorrelation in intraday returns. These assumptions allow the VARHAC estimator to be employed in the estimation of daily realised volatility. An empirical analysis of the VARHAC daily volatility estimator employing intraday transaction returns concludes that this estimator performs well in comparison to other estimators cited in the literature.     

Leverage and Volatility Feedback Effects in High-Frequency Data

We examine the relationship between volatility and past andfuture returns using high-frequency aggregate equity index data.Consistent with a prolonged "leverage" effect, we find the correlationsbetween absolute high-frequency returns and current and pasthigh-frequency returns to be significantly negative for severaldays, whereas the reverse cross-correlations are generally negligible.We also find that high-frequency data may be used in more accuratelyassessing volatility asymmetries over longer daily return horizons.Furthermore, our analysis of several popular continuous-timestochastic volatility models clearly points to the importanceof allowing for multiple latent volatility factors for satisfactorilydescribing the observed volatility asymmetries.     

Fundamentalists,chartists and asset pricing anomalies

This paper investigates whether excess volatility of asset prices and serial correlations of stock monthly returns may be explained by the interactions between fundamentalists and chartists. Fundamentalists forecast future prices cum dividends through an adaptive learning rule. In contrast, chartists forecast future prices based on the observation of past price movements. Numerical simulations reveal that the interplay of fundamentalists and chartists robustly generates excess volatility of asset prices, volatility clustering, trends in prices (i.e. positive serial correlations of returns) over short horizons and oscillations in prices (i.e. negative serial correlations of returns) over long horizons, often observed in financial data. Moreover, we find that the memory of the learning rule plays a key role in explaining the above-mentioned stylized facts. In particular, we establish that excess volatility of asset prices; volatility clustering and autocorrelation of returns at different horizons emerge when fundamentalists have short memory. However, volatility clustering as well as short-run and long-run dependencies, observed in financial time series, are more pronounced when fundamentalists have longer memory.     

The usefulness of cross-sectional dispersion for forecasting aggregate stock price volatility

Does cross-sectional dispersion in the returns of different stocks help forecast volatility of the S&P 500 index? This paper develops a model of stock returns where dispersion in returns across different stocks is modeled jointly with aggregate volatility. Although specifications that allow for feedback from cross-sectional dispersion to aggregate volatility have a better fit in sample, they prove not to be robust for purposes of out-of-sample forecasting. Using a full cross-section of stock returns jointly, however, I find that use of cross-sectional dispersion can help improve parameter estimates of a GARCH process for aggregate volatility to generate better forecasts both in sample and out of sample. Given this evidence, I conclude that cross-sectional information helps predict market volatility indirectly rather than directly entering in the data-generating process.     

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.     

Additional evidence on transparency and bank financial performance

This paper examines the relationship between volatility and the probability of occurrence of expected extreme returns in the Canadian market. Four measures of volatility are examined: implied volatility from firm option prices, conditional volatility calculated using an EGARCH model, idiosyncratic volatility, and expected shortfall. A significantly positive relationship is observed between a firm's idiosyncratic volatility and the probability of occurrence of an extreme return in the subsequent month for firms. A 10% increase in idiosyncratic volatility in a given month is associated with the probability of an extreme shock in the subsequent month (top or bottom 1.5% of the returns distribution) of 26.4%. Other firm characteristics, including firm age, price, volume and book‐to‐market ratio, are also shown to be significantly related to subsequent firm extreme returns. The effects of conditional and implied volatility are mixed. The E‐GARCH and expected shortfall measures of conditional volatility are consistent with mean reversion: high short term realizations of conditional volatility foreshadow a lower probability of extreme returns.     

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.     

Pricing methods and hedging strategies for volatility derivatives

We explore the valuation and hedging of discretely observed volatility derivatives using three different models for the price of the underlying asset: Geometric Brownian motion with constant volatility, a local volatility surface, and jump-diffusion. We begin by comparing the effects on valuation of variations in contract design, such as the differences between specifying log returns or actual returns and incorporating caps on the level of realized volatility. We then focus on the difficulties associated with hedging these products. Delta hedging strategies are ineffective for hedging volatility derivatives since they require very frequent rebalancing. Moreover, they provide limited protection in the jump-diffusion context. We study the performance of a hedging strategy for volatility swaps that establishes small, fixed positions in vanilla options at each volatility observation.     

Portfolio Returns,Market Volatility,and Seasonality

This paper examines three important issues related to the relationship between stock returns and volatility. First, are Duffee's (1995) findings of the relationship between individual stock returns and volatility valid at the portfolio level? Second, is there a seasonality of the market return volatility? Lastly, do size portfolio returns react symmetrically to the market volatility during business cycles? We find that the market volatility exhibits strong autocorrelation and small size portfolio returns exhibit seasonality. However, this phenomenon is not present in large size portfolios. For the entire sample period of 1962–1995, the highest average monthly volatility occurred in October, followed by November, and then January. Examining the two sub-sample periods, we find that the average market volatility increases by 15.4% in the second sample period of 1980–1995 compared to the first sample period of 1962–1979. During the contraction period, the average market volatility is 60.9% higher than that during the expansion period. Using a binary regression model, we find that size portfolio returns react asymmetrically with the market volatility during business cycles. This paper documents a strongly negative contemporaneous relationship between the size portfolio returns and the market volatility that is consistent with the previous findings at the aggregate level, but is inconsistent with the findings at the individual firm level. In contrast with the previous findings, however, we find an ambiguous relationship between the percentage change in the market volatility and the contemporaneous stock portfolio returns. This ambiguity is attributed to strongly negative contemporaneous and one-month ahead relationships between the market volatility and portfolio returns.

     

The Dynamic Relation Between Stock Returns, Trading Volume, and Volatility

We examine the dynamic relation between returns, volume, and volatility of stock indexes. The data come from nine national markets and cover the period from 1973 to 2000. The results show a positive correlation between trading volume and the absolute value of the stock price change. Granger causality tests demonstrate that for some countries, returns cause volume and volume causes returns. Our results indicate that trading volume contributes some information to the returns process. The results also show persistence in volatility even after we incorporate contemporaneous and lagged volume effects. The results are robust across the nine national markets.     

Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility

The paper develops an empirical return volatility-trading volume model from a microstructure framework in which informational asymmetries and liquidity needs motivate trade in response to information arrivals. The resulting system modifies the so-called “Mixture of Distribution Hypothesis” (MDH). The dynamic features are governed by the information flow, modeled as a stochastic volatility process, and generalize standard ARCH specifications. Specification tests support the modified MDH representation and show that it vastly outperforms the standard MDH. The findings suggest that the model may be useful for analysis of the economic factors behind the observed volatility clustering in returns.     

Forecasting daily exchange rate volatility using intraday returns

This study investigates whether intraday returns contain important information for forecasting daily volatility. Whereas in the existing literature volatility models for daily returns are improved by including intraday information such as the daily high and low, volume, the number of trades, and intraday returns, here the volatility of intraday returns is explicitly modelled. Daily volatility forecasts are constructed from multiple volatility forecasts for intraday intervals. It is shown for the DEM/USD and the YEN/USD exchange rates that this results in superior forecasts for daily volatility.     

Implications of market microstructure for realized variance measurement

Volatility measuring and estimation based on intra-day high-frequency data has grown in popularity during the last few years. A significant part of the research uses volatility and variance measures based on the sum of squared high-frequency returns. These volatility measures, introduced and mathematically justified in a series of papers by Andersen et al. [1999. (Understanding, optimizing, using and forecasting) realized volatility and correlation. Leonard N. Stern School Finance Department Working Paper Series, 99-061, New York University; 2000a. The distribution of realized exchange rate volatility. Journal of the American Statistical Association 96, no. 453: 42–55; 2000b. Exchange rate returns standardized by realized volatility are (nearly) Gaussian. Multinational Finance Journal 4, no. 3/4: 159–179; 2003. Modeling and forecasting realized volatility. NBER Working Paper Series 8160.] and Andersen et al. 2001a. Modeling and forecasting realized volatility. NBER Working Paper Series 8160., are referred to as ‘realized variance’. From the theory of quadratic variations of diffusions, it is possible to show that realized variance measures, based on sufficiently frequently sampled returns, are error-free volatility estimates. Our objective here is to examine realized variance measures, where well-documented market microstructure effects, such as return autocorrelation and volatility clustering, are included in the return generating process. Our findings are that the use of squared returns as a measure for realized variance will lead to estimation errors on sampling frequencies adopted in the literature. In the case of return autocorrelation, there will be systematic biases. Further, we establish increased standard deviation in the error between measured and real variance as sampling frequency decreases and when volatility is non-constant.     

Volatility spreads and earnings announcement returns

Prior research documents that volatility spreads predict stock returns. If the trading activity of informed investors is an important driver of volatility spreads, then the predictability of stock returns should be more pronounced during major information events. This paper investigates whether the predictability of equity returns by volatility spreads is stronger during earnings announcements. Volatility spreads are measured by the implied volatility differences between pairs of strike price and expiration date matched put and call options and capture price pressures in the option market. During a two-day earnings announcement window, the abnormal returns to the quintile that includes stocks with relatively expensive call options is more than 1.5% greater than the abnormal returns to the quintile that includes stocks with relatively expensive put options. This result is robust after measuring volatility spreads in alternative ways and controlling for firm characteristics and lagged equity returns. The degree of announcement return predictability is stronger when volatility spreads are measured using more liquid options, the information environment is more asymmetric, and stock liquidity is low.     

Carry Trades and Global Foreign Exchange Volatility

We investigate the relation between global foreign exchange (FX) volatility risk and the cross section of excess returns arising from popular strategies that borrow in low interest rate currencies and invest in high interest rate currencies, so‐called “carry trades.” We find that high interest rate currencies are negatively related to innovations in global FX volatility, and thus deliver low returns in times of unexpected high volatility, when low interest rate currencies provide a hedge by yielding positive returns. Furthermore, we show that volatility risk dominates liquidity risk and our volatility risk proxy also performs well for pricing returns of other portfolios.     

News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns

This paper models components of the return distribution, which are assumed to be directed by a latent news process. The conditional variance of returns is a combination of jumps and smoothly changing components. A heterogeneous Poisson process with a time‐varying conditional intensity parameter governs the likelihood of jumps. Unlike typical jump models with stochastic volatility, previous realizations of both jump and normal innovations can feed back asymmetrically into expected volatility. This model improves forecasts of volatility, particularly after large changes in stock returns. We provide empirical evidence of the impact and feedback effects of jump versus normal return innovations, leverage effects, and the time‐series dynamics of jump clustering.     

Empirical analysis of real and financial volatilities on stock excess returns: evidence from Taiwan industrial data

This paper tests the relation between stock excess returns and risk factors measured by volatility. The sources of the volatility are based on the volatility of macroeconomic factors and time-series volatility. To model the macroeconomic fundamentals, we divide the risk into real and financial volatilities pertinent to Taiwan's economic environment. By examining the data of indusry excess returns and market excess returns, we find evidence to reject the hypothesis that the stock excess returns are independent of the real and financial volatilities.     

Growth uncertainty,generalized disappointment aversion and production-based asset pricing

We study a production economy with regime switching in the conditional mean and volatility of productivity growth. The representative agent has generalized disappointment aversion (GDA) preferences. We show that volatility risk in productivity growth carries a positive and sizable risk premium in levered equity. Our model can endogenously generate long-run risks in the volatility of consumption growth observed in the data. We show that introducing leverage with a procyclical dividend process consistent with the data is critical for the GDA preferences to have a large impact on equity returns.