Correlation Smile, Volatility Skew and Systematic Risk Sensitivity of Tranches.

Abstract

The classical way of treating the correlation smile phenomenon with credit index
tranches is to choose a sufficiently flexible model and fit it to tranche market prices. In
this article we go a step further and try to explain the tranche prices more
fundamentally without directly fitting them. To this end, we use a risk neutral measure
of the market factor which we derive from equity index options. The resulting model
allows separating the premium for correlation risk from the premium for catastrophe or
down-side risk. We show that ignoring the high correlation risk of tranches but allowing
for their down-side risk explains the historical market prices fairly well. By contrast, the
standard Gaussian copula model allows for the high correlation risk of tranches but
disregards the specific down-side risk premia.