Zusammenfassung
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, the authors go a step further and try to explain the tranche prices more fundamentally without directly fitting them. To this end, they use a risk-neutral measure of the market factor that we derive from equity ...
Zusammenfassung
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, the authors go a step further and try to explain the tranche prices more fundamentally without directly fitting them. To this end, they use a risk-neutral measure of the market factor that we derive from equity index options. The resulting model allows separating the premium for correlation risk from the premium for catastrophe or downside risk. They show that ignoring the high correlation risk of tranches but allowing for their downside 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 downside risk premia.
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