Contingencies Online - November/December 2010

exposure and residual components stay the same. If, for example, the common-factor volatility increases to 30 percent, total asset volatility will rise to 33 percent and correlation will rise to 82 percent. This should not be a surprise: An abnormally volatile common component is driving all asset prices. Figure 4 shows the impact of different assumptions for the volatility of the common factor on total asset risk and correlation. You can see that “stress” (high common-factor volatility) is associated naturally with highly elevated correlation.

implementation and future Challenges
To generate the equity tail dependence and the elevated cor-
relation observed at times of stress, one possibility is to allow
stochastic variation in the volatility of a factor shared by all
equity markets. This isn’t a new idea. You easily can argue
that it’s just common sense, since it builds directly into the
model what can be observed across equity markets over long
time horizons—long benign periods punctuated by episodes of
extreme instability, most often common to many markets. In-
deed, modelers do offer stochastic models for common-factor
volatility that are driven by both a continuous time compo-
nent and a discontinuous “jump” component. In practice, the
implementation of these models is more subtle than described
above. If the modeler correlates shocks (up) to volatility with
falls in asset prices, it’s possible simultaneously to build nega-
tive skewness into asset returns alongside the excess kurtosis
(fat tails) and tail dependency generated by this class of model.

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