Modeling default and prepayment using Lévy processes: An application to asset backed securities

H. Jönsson, W. Schoutens, G. Damme, van

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The securitization of financial assets is a form of structured finance, developed by the U.S. banking world in the early 1980's (in Mortgage-Backed-Securities format) in order to reduce regulatory capital requirements by removing and transferring risk from the balance sheet to other parties. Today, virtually any form of debt obligations and receivables has been securitised, resulting in an approximately $2.5 trillion ABS outstanding in the U.S. alone: a market which is rapidly spreading to Europe, Latin-America and Southeast Asia. Though no two ABS contracts are the same and therefore each deal requires its very own model, there are three important features which appear in virtually any securitization deal: default risk, Loss-Given-Default and prepayment risk. In this paper we will only be concerned with default and prepayment and discuss a number of traditional (continuous) and Levy-based (pure jump) methods for modelling the latter risks. After briefly explaining the methods and their underlying intuition, the models are applied to a simple ABS deal in order to determine the rating of the notes. It turns out that the pure jump models produce lower (i.e. more conservative) ratings than the traditional methods (e.g. Vasicek), which are clearly incapable of capturing the shock-driven nature of losses and prepayments.
Original languageEnglish
Title of host publicationAdvanced Financial Modelling
EditorsH. Albrecher, W.J. Runggaldier, W. Schachermayer
Place of PublicationBerlin
PublisherWalter de Gruyter GmbH
ISBN (Print)978-3-11-021313-3
Publication statusPublished - 2009

Publication series

NameRadon Series on Computational and Applied Mathematics


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