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On the White Board - February 2010
Feb 15, 2010
Since the CDS Big Bang
After Lehman fell, the financial world realized that the CDS market was tying together everyone's fates unnecessarily. In particular, because the size of CDS spread payments changed daily, it was nearly impossible to offset long-term contracts, and thus the counter-party risk was long-standing. The "CDS Big Bang" was created to solve this problem: since Spring 2009, CDS quarterly payments have been standardized, making offsetting easy. The complication is that, whereas the CDS contracts used to be worth no money upon entering, there is now an "upfront price" to be paid at the beginning. We at RiskMetrics have been working on revamping our CDS risk methodology to deal with this new market data.
This upfront price can be negative or positive, which means that when we want to define a return on a CDS it doesn't make too much sense to do it directly on the upfront price, as either log or relative returns would run the risk of being undefined, if say the upfront is zero. For that reason, we first shift the upfront price into positive territory. After shifting, our upfront is equivalent to the price of the CDS contract if the buyer of the protection paid all the spread payments today. Then since this will always be positive, we can (and do) define the return as the relative return of this time series.
Figure 1 - All IG
Once we have the above definition, we can look at the empirical distribution of volatility-normalized daily returns for, say, the 125 investment grade constituents of the North American Investment Grade Index (see first plot above). The empirical distribution is far from normal; in fact it closely resembles a double exponential, or Laplacian, distribution. The same phenomenon holds true if we only look at one CDS instrument (see the analogous plot for just AIG in the second plot below). We are in the process of introducing a multivariate Laplacian distribution option for computing CDS Monte Carlo Value-at-Risk.
Figure 2 - AIG XR
Why is this distribution showing up here? First, why isn't it normal? Consider first a stock market index, where there are many winds blowing, pushing and pulling the index up and down, many of which cancel. A version of the Central Limit Theorem holds, at least heuristically, and we get a relatively normal (but still not completely normal) distribution for stock index returns because the index is a measurement of so many different things at once. By contrast, a CDS in some sense is a pure measurement of exactly one thing (or at least may be seen that way by credit traders)- namely, the risk of default of the underlying entity. Next, why is it Laplacian? On a given day, there is either news in the market which affects the market’s perception of the chances of a credit event, or there isn't. Say, for example, that credit traders consider most news irrelevant to credit events, even if it affects markets; this causes many more very small returns than a normal distribution would expect, as well as many more very large returns than a normal distribution (i.e. we see fat tails). Again, this at least heuristically describes the Laplacian distribution. There may be an even better explanation, as yet undiscovered.