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.
In our work, we have developed an asset-pricing model to study these market disruptions that 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 this past summer and early fall.
The DAX fell 30 percent from a high at the beginning of July to Oct. 4. Over the same period, the S&P fell 20 percent. 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.
Moreover, one can see the volatile nature of the distribution in 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.
• A large shock in asset prices today predicts further large, mean-reverting, shocks tomorrow.
• A large shock to aggregate market volatility predicts specific, directional clustering of country-level returns.
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 allows the distribution of volatility during disruptive periods to have fat-tails. Fat-tailed distributions, in contrast to a normal (or Gaussian) distribution, have greater probability for values further away from the average. They will have more extreme volatility movements than one would predict with the assumption of standard normality.
We now have ample data to test traditional models of returns and volatility thanks to the financial crisis and the debt turmoil in Europe.
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; James G. Scott is assistant professor of statistics at the McCombs School of Business at the University of Texas at Austin. The column was distributed by Bloomberg News.
