What good is a volatility model

doi:10.1088/1469-7688/1/2/305

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What good is a volatility model

Journal Article•DOI•

What good is a volatility model

01 Feb 2001-Quantitative Finance (Taylor & Francis Journals)-Vol. 1, Iss: 2, pp 237-245

TL;DR: In this article, the authors outline some stylized facts about volatility that should be incorporated in a model: pronounced persistence and mean-reversion, asymmetry such that the sign of an innovation also affects volatility and the possibility of exogenous or pre-determined variables influencing volatility.

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Abstract: A volatility model must be able to forecast volatility; this is the central requirement in almost all financial applications In this paper we outline some stylized facts about volatility that should be incorporated in a model: pronounced persistence and mean-reversion, asymmetry such that the sign of an innovation also affects volatility and the possibility of exogenous or pre-determined variables influencing volatility We use data on the Dow Jones Industrial Index to illustrate these stylized facts, and the ability of GARCH-type models to capture these features We conclude with some challenges for future research in this area

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Journal Article•DOI•

Is All That Talk Just Noise? The Information Content of Internet Stock Message Boards

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Werner Antweiler¹, Murray Z. Frank¹•Institutions (1)

University of British Columbia¹

01 Jun 2004-Journal of Finance

TL;DR: In this article, the authors studied the effect of more than 15 million messages posted on Yahoo! Finance and Raging Bull about the 45 companies in the Dow Jones Industrial Average and Dow Jones Internet Index Bullishness was measured using computational linguistics methods.

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Abstract: Financial press reports claim that Internet stock message boards can move markets We study the effect of more than 15 million messages posted on Yahoo! Finance and Raging Bull about the 45 companies in the Dow Jones Industrial Average and the Dow Jones Internet Index Bullishness is measured using computational linguistics methods Wall Street Journal news stories are used as controls We find that stock messages help predict market volatility Their effect on stock returns is statistically significant but economically small Consistent with Harris and Raviv (1993), disagreement among the posted messages is associated with increased trading volume MANY PEOPLE ARE DEVOTING a considerable amount of time and effort creating and reading the messages posted on Internet stock message boards News stories report that the message boards are having a significant impact on financial markets The Securities and Exchange Commission has prosecuted people for Internet messages All this attention to Internet stock messages caused us to wonder whether these messages actually contain financially relevant information 1 We consider three specific issues Does the number of messages posted or the bullishness of these messages help to predict returns? Is disagreement among the messages associated with more trades? Does the level of message posting or the bullishness of the messages help to predict volatility? The first issue is, does the level of message activity or the bullishness of the messages successfully predict subsequent stock returns? This is the natural starting place because a very high proportion of the messages contain explicit assertions that the particular stock is either a good buy or a bad buy Of course, there are a great many previous empirical studies showing how hard it is to predict stock returns by enough to cover transactions costs We find that there is evidence of a small degree of negative predictability even after controlling for bid‐ask bounce When many messages are posted on a given day, there ∗ Both authors are at the Sauder School of Business, University of British Columbia We would

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1,465 citations

Journal Article•DOI•

A forecast comparison of volatility models: does anything beat a GARCH(1,1)?

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Peter Reinhard Hansen¹, Asger Lunde²•Institutions (2)

Brown University¹, Aarhus University²

01 Dec 2005-Journal of Applied Econometrics

TL;DR: The authors compare 330 ARCH-type models in terms of their ability to describe the conditional variance and find no evidence that a GARCH(1,1) is outperformed by more sophisticated models in their analysis of exchange rates.

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Abstract: We compare 330 ARCH-type models in terms of their ability to describe the conditional variance. The models are compared out-of-sample using DM–$ exchange rate data and IBM return data, where the latter is based on a new data set of realized variance. We find no evidence that a GARCH(1,1) is outperformed by more sophisticated models in our analysis of exchange rates, whereas the GARCH(1,1) is clearly inferior to models that can accommodate a leverage effect in our analysis of IBM returns. The models are compared with the test for superior predictive ability (SPA) and the reality check for data snooping (RC). Our empirical results show that the RC lacks power to an extent that makes it unable to distinguish ‘good’ and ‘bad’ models in our analysis. Copyright © 2005 John Wiley & Sons, Ltd.

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1,254 citations

Journal Article•DOI•

A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?

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Peter Reinhard Hansen¹, Peter Reinhard Hansen², Peter Reinhard Hansen³, Asger Lunde³•Institutions (3)

University of North Carolina at Chapel Hill¹, Copenhagen Business School², Aarhus University³

22 Mar 2004-Social Science Research Network

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Abstract: We compare 330 ARCH-type models in terms of their ability to describe the conditional variance. The models are compared out-of-sample using DM-$ exchange rate data and IBM return data, where the latter is based on a new data set of realized variance. We find no evidence that a GARCH(1,1) is outperformed by more sophisticated models in our analysis of exchange rates, whereas the GARCH(1,1) is clearly inferior to models that can accommodate a leverage effect in our analysis of IBM returns. The models are compared with the test for superior predictive ability (SPA) and the reality check for data snooping (RC). Our empirical results show that the RC lacks power to an extent that makes it unable to distinguish 'good' and 'bad' models in our analysis.

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1,045 citations

Journal Article•DOI•

The Sum of All FEARS: Investor Sentiment and Asset Prices

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Zhi Da¹, Joseph Engelberg², Pengjie Gao¹•Institutions (2)

University of Notre Dame¹, University of California, San Diego²

06 Mar 2013-Social Science Research Network

TL;DR: In this article, the authors use the daily internet search volume from millions of households to reveal market-level sentiment, by aggregating the volume of queries related to household concerns (e.g. "recession", "unemployment" and "bankruptcy") and construct a Financial and Economic Attitudes Revealed by Search (FEARS) index as a new measure of investor sentiment.

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Abstract: We use the daily internet search volume from millions of households to reveal market-level sentiment. By aggregating the volume of queries related to household concerns (e.g. "recession", "unemployment" and "bankruptcy"), we construct a Financial and Economic Attitudes Revealed by Search (FEARS) index as a new measure of investor sentiment. Between 2004 and 2011, we find increases in FEARS lead to return reversals: although high FEARS are associated with low returns today, they predict high returns over the following two days. In the cross-section of stocks, the reversal effect is strongest among stocks which are attractive to noise traders and hard to arbitrage. FEARS also coincide with excess volatility and predict daily mutual fund flow. When FEARS increase, investors are more likely to pull money out of equity mutual funds and put it into bond funds. Taken together, the results are broadly consistent with theories of investor sentiment.

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774 citations

Cites background from "What good is a volatility model"

...Volatility is well-known to be persistent and long-lived (Engel and Patton (2001) and Andersen et al. (2001)) so we model this long-range dependence through the fractional integrated autoregressive moving average model, ( ), which allows us to extract innovations in volatility....
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...Since volatility is persistent and long-lived (Engel and Patton (2001) and Andersen et al. (2001)), we model this long-range dependence through the fractional integrated autoregressive moving average model, ( ) : Φ () (1− ) = Θ () (6) where the autoregressive coefficient is , fractional…...
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Journal Article•DOI•

The Sum of All FEARS Investor Sentiment and Asset Prices

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Zhi Da¹, Joseph Engelberg², Pengjie Gao¹•Institutions (2)

Mendoza College of Business¹, University of California, San Diego²

01 Jan 2015-Review of Financial Studies

TL;DR: In this paper, the authors use daily Internet search volume from millions of households to reveal market-level sentiment and predict short-term return reversals, temporary increases in volatility, and mutual fund flows out of equity funds and into bond funds.

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Abstract: We use daily Internet search volume from millions of households to reveal market-level sentiment. By aggregating the volume of queries related to household concerns (e.g., �recession,� �unemployment,� and �bankruptcy�), we construct a Financial and Economic Attitudes Revealed by Search (FEARS) index as a new measure of investor sentiment. Between 2004 and 2011, we find FEARS (i) predict short-term return reversals, (ii) predict temporary increases in volatility, and (iii) predict mutual fund flows out of equity funds and into bond funds. Taken together, the results are broadly consistent with theories of investor sentiment.

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712 citations

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References

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Journal Article•DOI•

Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation

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Robert F. Engle

01 Jul 1982-Econometrica

TL;DR: In this article, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced, which are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances.

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Abstract: Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced in this paper. These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance. A regression model is then introduced with disturbances following an ARCH process. Maximum likelihood estimators are described and a simple scoring iteration formulated. Ordinary least squares maintains its optimality properties in this set-up, but maximum likelihood is more efficient. The relative efficiency is calculated and can be infinite. To test whether the disturbances follow an ARCH process, the Lagrange multiplier procedure is employed. The test is based simply on the autocorrelation of the squared OLS residuals. This model is used to estimate the means and variances of inflation in the U.K. The ARCH effect is found to be significant and the estimated variances increase substantially during the chaotic seventies.

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20,728 citations

Journal Article•DOI•

Generalized autoregressive conditional heteroskedasticity

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Tim Bollerslev¹, Tim Bollerslev²•Institutions (2)

University of California, San Diego¹, Aarhus University²

01 Apr 1986-Journal of Econometrics

TL;DR: In this paper, a natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in 1982 to allow for past conditional variances in the current conditional variance equation is proposed.

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17,555 citations

Journal Article•DOI•

Conditional heteroskedasticity in asset returns: a new approach

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Daniel B. Nelson

01 Mar 1991-Econometrica

TL;DR: In this article, an exponential ARCH model is proposed to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987, which is an improvement over the widely-used GARCH model.

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Abstract: This paper introduces an ARCH model (exponential ARCH) that (1) allows correlation between returns and volatility innovations (an important feature of stock market volatility changes), (2) eliminates the need for inequality constraints on parameters, and (3) allows for a straightforward interpretation of the "persistence" of shocks to volatility. In the above respects, it is an improvement over the widely-used GARCH model. The model is applied to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987. Copyright 1991 by The Econometric Society.

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10,019 citations

"What good is a volatility model" refers background or methods in this paper

...This model was proposed by Glosten et al (1993) and Zakoian (1994) and was motivated by the EGARCH model of Nelson (1991). ht = ω+ p∑ i=1 αi(Rt−i−µ)2+ q∑ j=1 βjht−j + r∑ k=1 δt−kγk(Rt−k−µ)2 (19) where δt−k is an indicator variable, taking the value one if the residual at time t − k was negative,…...
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...Black (1976), Christie (1982), Nelson (1991), Glosten et al (1993) and Engle and Ng (1993) all find evidence of volatility being negatively related to equity returns....
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...A widely used class of models for the conditional volatility is the autoregressive conditionally heteroskedastic class of models introduced by Engle (1982), and extended by Bollerslev (1986), Engle et al (1987), Nelson (1991), Glosten et al (1993), amongst many others....
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Journal Article•DOI•

The behavior of stock market prices

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Eugene F. Fama

01 Jan 1965-The Journal of Business

8,252 citations

"What good is a volatility model" refers background in this paper

...Mandelbrot (1963) and Fama (1965) both reported evidence that large changes in the price of an asset are often followed by other large changes, and small changes are often followed by small changes....
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Journal Article•DOI•

On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks

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Lawrence R. Glosten, Ravi Jagannathan, David E. Runkle

01 Dec 1993-Journal of Finance

TL;DR: In this article, a modified GARCH-M model was used to find a negative relation between conditional expected monthly return and conditional variance of monthly return, using seasonal patterns in volatility and nominal interest rates to predict conditional variance.

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Abstract: We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility. THE TRADEOFF BETWEEN RISK and return has long been an important topic in asset valuation research. Most of this research has examined the tradeoff between risk and return among different securities within a given time period. The intertemporal relation between risk and return has been examined by several authors-Fama and Schwert (1977), French, Schwert, and Stambaugh (1987), Harvey (1989), Campbell and Hentschel (1992), Nelson (1991), and Chan, Karolyi, and Stulz (1992), to name a few. This paper extends that research.

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7,837 citations

"What good is a volatility model" refers background or methods or result in this paper

...This result confirms that of Glosten et al (1993) who also find that the Treasury bill rate is positively related to equity return volatility....
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...Andersen and Bollerslev (1998a), for example, find that the volatility of the Deutsche Mark– Dollar exchange rate increases markedly around the time of the announcement of US macroeconomic data, such as the Employment Report, the Producer Price Index or the quarterly GDP. Glosten et al (1993) find that indicator variables for October and January assist in explaining some of the dynamics of the conditional volatility of equity returns....
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...This result confirms that of Glosten et al. (1993) who also find that the Treasury bill rate is positively related to equity return volatility....
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...…markedly around the time of the announcement of US macroeconomic data, such as the Employment Report, the Producer Price Index or the quarterly GDP. Glosten et al (1993) find that indicator variables for October and January assist in explaining some of the dynamics of the conditional volatility…...
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...This model was proposed by Glosten et al (1993) and Zakoian (1994) and was motivated by the EGARCH model of Nelson (1991). ht = ω+ p∑ i=1 αi(Rt−i−µ)2+ q∑ j=1 βjht−j + r∑ k=1 δt−kγk(Rt−k−µ)2 (19) where δt−k is an indicator variable, taking the value one if the residual at time t − k was negative,…...
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