Arbitrage-Free Loss Surface Closest to Base Correlations

The drawbacks of base correlations are well-known to quantitative credit practitioners. The loss surface produced by any of its common implementations is arbitrageable either in the loss dimension, or the time dimension, or both. Yet the approach has been quite popular in the industry, especially with correlation traders, not least for its ability to fit the standard tranche market by definition, unlike any of the widely known “bottomup” models. Consequently a large effort has been put into developing the base correlation framework into a workable pricing and risk management system, even though its fundamental problems were never resolved. In the present work we start from a typical base correlation loss surface and seek to rectify it by relaxing as few conditions as possible. By focusing on the areas where arbitrage occurs most often, we are able to obtain an arbitrage-free loss surface with minimum modifications and still price standard tranches within the bid-offer and most of the times, very close to the mid. The new framework generates a series of loss distributions, and thus naturally offers a solution to such issues as pricing thin tranches and parts of the capital structure outside the quoted detachment points, previously dealt with by interpolation and extrapolation of base correlations.