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59
Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test
 REVIEW OF FINANCIAL STUDIES
, 1988
"... In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (19621985) and for all subperiod for a variety of aggrega ..."
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Cited by 322 (15 self)
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In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (19621985) and for all subperiod for a variety of aggregate returns indexes and sizesorted portofolios. Although the rejections are due largely to the behavior of small stocks, they cannot be attributed completely to the effects of infrequent trading or timevarying volatilities. Moreover, the rejection of the random walk for weekly returns does not support a meanreverting model of asset prices.
Forecasting crashes: Trading volume, past returns and conditional skewness in stock prices
 JOURNAL OF FINANCIAL ECONOMICS
, 2001
"... This paper is an investigation into the determinants of asymmetries in stock returns. We develop a series of crosssectional regression specifications which attempt to forecast skewness in the daily returns of individual stocks. Negative skewness is most pronounced in stocks that have experienced: ..."
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Cited by 50 (3 self)
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This paper is an investigation into the determinants of asymmetries in stock returns. We develop a series of crosssectional regression specifications which attempt to forecast skewness in the daily returns of individual stocks. Negative skewness is most pronounced in stocks that have experienced: 1) an increase in trading volume relative to trend over the prior six months; and 2) positive returns over the prior thirtysix months. The first finding is consistent with the model of Hong and Stein (1999), which predicts that negative asymmetries are more likely to occur when there are large differences of opinion among investors. The latter finding fits with a number of theories, most notably Blanchard and Watson’s (1982) rendition of stockprice bubbles. Analogous results also obtain when we attempt to forecast the skewness of the aggregate stock market, though our statistical power in this case is limited.
A DiscreteTime Model for Daily S&P500 Returns and Realized Variations: Jumps and Leverage Effects
, 2007
"... We develop an empirically highly accurate discretetime daily stochastic volatility model that explicitly distinguishes between the jump and continuoustime components of price movements using nonparametric realized variation and Bipower variation measures constructed from highfrequency intraday dat ..."
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Cited by 30 (2 self)
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We develop an empirically highly accurate discretetime daily stochastic volatility model that explicitly distinguishes between the jump and continuoustime components of price movements using nonparametric realized variation and Bipower variation measures constructed from highfrequency intraday data. The model setup allows us to directly assess the structural interdependencies among the shocks to returns and the two different volatility components. The model estimates suggest that the leverage effect, or asymmetry between returns and volatility, works primarily through the continuous volatility component. The excellent fit of the model makes it an ideal candidate for an easytoimplement auxiliary model in the context of indirect estimation of empirically more realistic continuoustime jump diffusion and Lévydriven stochastic volatility models, effectively incorporating the interdaily dependencies inherent in the highfrequency intraday data.
2001), The Pricing Kernel Puzzle: Reconciling Index Option Data and Economic Theory, Working Paper
"... One of the central questions in financial economics is the determination of asset prices, such as the value of a stock. Over the past three decades, research on this topic has converged on a concept called the “stateprice density”. However, a puzzle has arisen. On the one hand, Cox, Ingersoll, and ..."
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Cited by 26 (2 self)
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One of the central questions in financial economics is the determination of asset prices, such as the value of a stock. Over the past three decades, research on this topic has converged on a concept called the “stateprice density”. However, a puzzle has arisen. On the one hand, Cox, Ingersoll, and Ross (1985) and others argue that the ratio of the stateprice density to the statistical probability density, which is commonly known as the pricing kernel, should decrease monotonically as the aggregate wealth of an economy rises. On the other hand, recent empirical work on options on the S&P 500 index suggests that, for a sizable range of index levels, the pricing kernel is increasing instead of decreasing. We investigate theoretical explanations to this puzzle. Our existing work has ruled out some alternative hypotheses, such as data imperfections and methodological problems. The current paper focuses on the hypothesis of statedependent utility. Statedependent utility can arise from diverse causes such as habit persistence, stochastic index volatility, or dependence on interest rates or other asset prices. In this paper we characterize a general relation between the index and the state variables that is required to explain the puzzle. However, it remains for us to provide economic reasoning to justify this relation. The existing literature is largely unsatisfactory with respect to this puzzle, and most research does not touch on the puzzle altogether.
Nonlinear Features of Realized FX Volatility

, 2001
"... This paper investigates nonlinear features of FX volatility dynamics using estimates of daily volatility based on the sum of intraday squared returns. Measurement errors associated with using realized volatility to measure ex post latent volatility imply that standard time series models of the condi ..."
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Cited by 15 (1 self)
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This paper investigates nonlinear features of FX volatility dynamics using estimates of daily volatility based on the sum of intraday squared returns. Measurement errors associated with using realized volatility to measure ex post latent volatility imply that standard time series models of the conditional variance become variants of an ARMAX model. We explore nonlinear departures from these linear specifications using a doubly stochastic process under durationdependent mixing. This process can capture large abrupt changes in the level of volatility, timevarying persistence, and timevarying variance of volatility. The results have implications for forecast precision, hedging, and pricing of derivatives.
Multifrequency News and Stock Returns
, 2006
"... Aggregate stock prices are driven by shocks with persistence levels ranging from daily intervals to several decades. To accommodate this, we introduce a parsimonious equilibrium with regimeshifts of heterogeneous durations in dividend news, and estimate specifications with up to 256 states on daily ..."
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Cited by 15 (4 self)
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Aggregate stock prices are driven by shocks with persistence levels ranging from daily intervals to several decades. To accommodate this, we introduce a parsimonious equilibrium with regimeshifts of heterogeneous durations in dividend news, and estimate specifications with up to 256 states on daily U.S. equity returns. The multifrequency equilibrium has significantly higher likelihood than the classic Campbell and Hentschel (1992) specification, while generating volatility feedback effects 10 to 40 times larger. Furthermore, Bayesian learning about volatility generates a novel tradeoff between skewness and kurtosis as information quality varies, which complements the traditional uncertainty channel (e.g., Veronesi, 1999). Economies with intermediate investor information best match the return data.
Do bonds span volatility risk in the U.S. Treasury market? A speci test of ane term structure models, Working paper
, 2006
"... Further, we thank Mitch Haviv of GovPX for providing useful information on their data. Of course, all errors remain our sole responsibility. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Chicago, the Federal Reserve System, or the Nation ..."
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Cited by 12 (0 self)
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Further, we thank Mitch Haviv of GovPX for providing useful information on their data. Of course, all errors remain our sole responsibility. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Chicago, the Federal Reserve System, or the National
Asymptotic Theory for RangeBased Estimation of Integrated Variance of a Continuous SemiMartingale, working paper, Aarhus School of Business
, 2005
"... We provide a set of probabilistic laws for rangebased estimation of integrated variance of a continuous semimartingale. To accomplish this, we exploit the properties of the price range as a volatility proxy and suggest a new method for nonparametric measurement of return variation. Assuming the e ..."
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Cited by 11 (0 self)
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We provide a set of probabilistic laws for rangebased estimation of integrated variance of a continuous semimartingale. To accomplish this, we exploit the properties of the price range as a volatility proxy and suggest a new method for nonparametric measurement of return variation. Assuming the entire sample path realization of the logprice process is available and given weak technical conditions we prove that the highlow statistic converges in probability to the integrated variance. Moreover, with slightly stronger conditions, in particular a zero driftterm, we find an asymptotic distribution theory. To relax the meanzero constraint, we modify the estimator using an adjusted range. A weak law of large numbers and central limit theorem is then derived under more general assumptions about drift. In practice, inference about integrated variance is drawn from discretely sampled data. Here, we split the sampling period into subintervals containing the same number of price recordings and estimate the true range. In this setting, we also prove consistency and asymptotic normality. Finally, we analyze our framework in the presence of microstructure noise. JEL Classification: C10; C22; C80.
Predictable Dynamics in the S&P 500 Index Options Implied Volatility Surface”, working paper
, 2003
"... One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of Þtting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, re ..."
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Cited by 7 (2 self)
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One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of Þtting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, recent empirical evidence suggests that the parameters characterizing the IVS change over time. In this paper we study whether the resulting predictability patterns in the IVS coefficients may be exploited in practice. We propose a twostage approach to modeling and forecasting the S&P 500 index options IVS. In the Þrst stage we model the surface along the crosssectional moneyness and timetomaturity dimensions, similarly to Dumas et al. (1998). In the secondstage we model the dynamics of the crosssectional Þrststage implied volatility surface coefficients by means of vector autoregression models. We Þnd that not only the S&P 500 implied volatility surface can be successfully modeled, but also that its movements over time are highly predictable in a statistical sense. We then examine the economic signiÞcance of this statistical predictability with mixed Þndings. Whereas proÞtable deltahedged positions can be set up that exploit the dynamics captured by the model under moderate transaction costs and when trading rules are selective in terms of expected gains from the trades, most of this proÞtability disappears when we increase the level of transaction costs and trade multiple contracts off wide segments of the IVS. This suggests that predictability of the timevarying S&P 500 implied volatility surface may be not inconsistent with market efficiency.