ARCH modeling in finance: A review of the theory and empirical evidence

A voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using ARCH and stochastic volatility models. While most of these studies have documented highly significant in-sample parameter estimates and pronounced intertemporal volatility persistence, traditional ex-post forecast evaluation criteria suggest that the models provide seemingly poor volatility forecasts. Contrary to this contention, we show that volatility models produce strikingly accurate interdaily forecasts for the latent volatility factor that would be of interest in most financial applications. New methods for improved ex-post interdaily volatility measurements based on high-frequency intradaily data are also discussed.

https://faculty.washington.edu/ezivot/econ589//////AndersenBollerslevIER1998.pdf

Answering the skeptics: yes, standard volatility models do provide accurate forecasts*

This paper defines the news impact curve which measures how new information is incorporated into volatility estimates. Various new and existing ARCH models including a partially nonparametric one are compared and estimated with daily Japanese stock return data. New diagnostic tests are presented which emphasize the asymmetry of the volatility response to news. Our results suggest that the model by Glosten, Jagannathan, and Runkle is the best parametric model. The EGARCH also can capture most of the asymmetry; however, there is evidence that the variability of the conditional variance implied by the EGARCH is too high.

/pdf/measuring-and-testing-the-impact-of-news-on-volatility-533bchskmf.pdf

Measuring and Testing the Impact of News on Volatility

We examine the pricing of aggregate volatility risk in the cross-section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. In addition, we find that stocks with high idiosyncratic volatility relative to the Fama and French (1993) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility.

The Cross-Section of Volatility and Expected Returns

We examine the pricing of aggregate volatility risk in the cross-section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the Fama and French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility. IT IS WELL KNOWN THAT THE VOLATILITY OF STOCK RETURNS varies over time. While considerable research has examined the time-series relation between the volatility of the market and the expected return on the market (see, among others, Campbell and Hentschel (1992) and Glosten, Jagannathan, and Runkle (1993)), the question of how aggregate volatility affects the cross-section of expected stock returns has received less attention. Time-varying market volatility induces changes in the investment opportunity set by changing the expectation of future market returns, or by changing the risk-return trade-off. If the volatility of the market return is a systematic risk factor, the arbitrage pricing theory or a factor model predicts that aggregate volatility should also be priced in the cross-section of stocks. Hence, stocks with different sensitivities to innovations in aggregate volatility should have different expected returns. The first goal of this paper is to provide a systematic investigation of how the stochastic volatility of the market is priced in the cross-section of expected stock returns. We want to both determine whether the volatility of the market

https://www0.gsb.columbia.edu/faculty/rhodrick/crosssection.pdf

Stock market volatility and the information content of stock index options

Following the leader: ☆: a study of individual analysts’ earnings forecasts

Earnings management and firm valuation under asymmetric information

This paper documents significantly negative stock price reactions to shareholder initiated class action lawsuits. We find that shareholders partially anticipate these lawsuits based on lawsuit filings against other firms in the same industry and capitalize part of these losses prior to a lawsuit filing date. We show that the more likely a firm is to be sued, the larger is the partial anticipation effect (shareholder losses capitalized prior to a lawsuit filing date) and smaller is the filing date effect (shareholder losses measured on the lawsuit filing date). Our evidence suggests that previous research that typically focuses on the filing date effect understates the magnitude of shareholder losses, and such an understatement is greater for firms with a higher likelihood of being sued.

Shareholder Initiated Class Action Lawsuits: Shareholder Wealth Effects and Industry Spillovers

This paper documents significantly negative stock price reactions to shareholder-initiated class action lawsuits. We find that shareholders partially anticipate these lawsuits based on lawsuit filings against other firms in the same industry and capitalize part of these losses prior to a lawsuit filing date. We show that the more likely a firm is to be sued, the larger the partial anticipation effect (shareholder losses capitalized prior to a lawsuit filing date) and the smaller the filing date effect (shareholder losses measured on the lawsuit filing date). Our evidence suggests that previous research that typically focuses on the filing date effect understates the magnitude of shareholder losses, and that such an understatement is greater for firms with a higher likelihood of being sued.

/pdf/shareholder-initiated-class-action-lawsuits-shareholder-3rvakbk09y.pdf

Craig M. Lewis

Papers

Stock market volatility and the information content of stock index options

Following the leader: ☆: a study of individual analysts’ earnings forecasts

Earnings management and firm valuation under asymmetric information

Shareholder Initiated Class Action Lawsuits: Shareholder Wealth Effects and Industry Spillovers

Shareholder-Initiated Class Action Lawsuits: Shareholder Wealth Effects and Industry Spillovers