Base Expected Loss and Base Correlation Smile
The surest way to corrupt a youth is to instruct him to hold in higher esteem those who think alike than those who think differently.
Friedrich Nietzsche


In Chapter 9 we described the concepts of implied compound correlation and base correlation (BC), highlighting the reasons for the market adoption of the latter. That is, the pricing of tranches of the capital structure of a bespoke portfolio could not be done directly using compound correlation. It also meant that the ability to price bespoke tranches was determinant for the creation and use by market participants of the concept of base correlation. By using equity or base tranches the price of a tranche [A-D] is calculated using the two equity tranches with A and D as detachment points. Moreover, the BC concept makes it quite straightforward to bootstrap between two standard attachment points for pricing bespoke tranches.
The methodology, however, has some weaknesses. First of all, it is very sensitive to the interpolation technique used. Even worse, the methodology may not be arbitrage-free. It does not provide any guidance on how to extrapolate the curve, especially below the 3% attachment point. Additionally, a fundamental reason for the existence of the standardized credit indices is their use in the pricing discovery process of bespoke tranches of credit portfolios. Although the base correlation concept solves the problem of pricing bespoke tranches ...

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