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Georges Duponcheele, William Perraudin, Alastair Pickett, and Daniel Totouom-Tangho
This paper examines the effects of granularity and heterogeneity on capital requirements for securitisation transactions. For securitisation portfolios exhibiting a low number of obligors, a granularity adjustment to the Arbitrage Free Approach (AFA) (proposed by Duponcheele et al (2013a)) is derived in detail. The adjustment is based on a second-order moment matching of the loss distribution under the Vasicek approximation. Capital based on the AFA inclusive of granularity adjustments is compared with the capital implied by a Monte Carlo model. Similarly, for securitisation possessing heterogeneous pools (including barbell deals), the tranche capital implied by the AFA is compared with that obtained using a Monte Carlo model.
We conclude (i) that a simple version of the AFA, using pool level parameters, supplies accurate capital estimates even for extreme barbell deals, (ii) that the AFA, inclusive of granularity adjustments in the correlation, gives accurate capital measures for all except the few securitisation deals that have pools with fewer than 10 effective assets, and (iii) that for such deals, the AFA, inclusive of granularity adjustments to both the correlation and the loss given- default rates gives a capital distribution that is compatible with the situation in which recovery rates of individual assets are stochastic.