The financial crisis and the meltdown in Europe have exposed the deficiencies of traditional asset-pricing models, particularly their inability to account for the effect of contagion from one market to another. The good news is that the length and the persistence of the turmoil have given researchers a trove of data to develop new predictive tools.

In our work, we developed an asset-pricing model to study these market disruptions, which incorporates random shocks to volatility that are correlated across markets. It provides a more accurate way to evaluate contagion, defined as the extent to which shocks from one market affect another over and above the level implied by the underlying asset-pricing model.

As an example of the volatility and correlation observed during the financial crisis, consider the movements in Germany’s DAX Index and the Standard & Poor’s 500 Index from July through early October 2011. The DAX fell 30 percent, to 5,216 on Oct. 4, from a high of 7,402 at the beginning of July. Over the same period, the S&P fell 20 percent, to 1,075, from 1,340; meanwhile the Chicago Board Options Exchange Volatility Index, known as the VIX, increased to 45.5 percent, from 15 percent.

Over the subsequent month and a half, volatility remained persistently higher than traditional asset-pricing models would have predicted, even though returns stabilized. The large drops in the DAX and S&P 500 reflect increases in the underlying asset-return volatilities. This is also directly observed in the increase in the VIX.

VIX Spike

Moreover, one can see the fat-tailed nature of the distribution of volatility in the daily movements. For example, on Nov. 10, after markets had stabilized somewhat, the VIX index spiked to above 36 percent, from 28 percent, an intraday move of more than 8 percent.

This episode captures the three facts about global markets that any asset-pricing model must now address:

-- A large shock in asset returns in one market predicts large shocks to other markets. This is cross-sectional clustering of shocks, which some researchers call “meteor shower” volatility.

-- A large shock in asset prices today predicts further large, mean-reverting, shocks tomorrow. This is a time-series or self-exciting clustering effect in volatility.

-- A large shock to aggregate market volatility predicts specific, directional clustering of country-level returns. Allowing for the effect of directional volatility is important for measuring contagion in markets.

Our asset-pricing model incorporates three volatility effects: cross-sectional clustering across countries (or markets), longitudinal clustering across time and directional clustering. These aren’t part of traditional models.

Cross-sectional clustering accounts for the observation that large market movements in one region seem to increase the chances of observing a large movement in another, beyond what would be predicted by traditional asset-pricing models.

Longitudinal clustering allows volatility shocks to persist over time, a well-known feature of such phenomena.

Directional clustering captures the fact that shocks in one market are often followed by shocks in a particular direction in another. That is, the event in the first market can be used to help predict the return in the other market. Our analysis finds that directional clustering has the greatest impact in predicting contagion between markets.

Fat-Tails

Our analysis allows the distribution of volatility during disruptive periods to have fat-tails. This is a characteristic that has long been recognized in the distribution of asset returns. Fat-tailed distributions, in contrast to a normal (or Gaussian) distribution, have greater probability for values further away from the average; fat-tailed distributions will have more extreme volatility movements than one would predict with the assumption of standard normality.

The inclusion of fat-tails has implications for the way contagion between markets is measured. Because contagion is the excess correlation between asset returns, it can only be properly evaluated if one begins with an asset pricing that incorporates fat-tailed volatility.

We now have ample data to test traditional models of returns and volatility thanks to the financial crisis and the debt turmoil in Europe. These events also have renewed interest in asset-pricing models as a method for measuring contagion effects across markets.

New models are needed to replace the old ones, whose simplistic assumptions about volatility cannot capture the current complex environment.

(Nicholas G. Polson is professor of econometrics and statistics at the University of Chicago Booth School of Business and a contributor to Business Class. James G. Scott is assistant professor of statistics at the McCombs School of Business at the University of Texas at Austin. The opinions expressed are their own.)

To contact the writers of this article: Nicholas G. Polson at Nicholas.polson@chicagobooth.edu; James G. Scott at james.scott@mccombs.utexas.edu.

To contact the editor responsible for this article: Max Berley at mberley@bloomberg.net.