Premium
DYNAMIC CDO TERM STRUCTURE MODELING
Author(s) -
Filipović Damir,
Overbeck Ludger,
Schmidt Thorsten
Publication year - 2011
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2010.00421.x
Subject(s) - collateralized debt obligation , bond , economics , arbitrage , term (time) , portfolio , credit derivative , econometrics , volatility (finance) , affine transformation , yield curve , heath–jarrow–morton framework , mathematical economics , itraxx , tranche , credit risk , financial economics , actuarial science , mathematics , credit valuation adjustment , collateral , finance , physics , pure mathematics , credit reference , quantum mechanics
This paper provides a unifying approach for valuing contingent claims on a portfolio of credits, such as collateralized debt obligations (CDOs). We introduce the defaultable ( T , x ) ‐bonds, which pay one if the aggregated loss process in the underlying pool of the CDO has not exceeded x at maturity T , and zero else. Necessary and sufficient conditions on the stochastic term structure movements for the absence of arbitrage are given. Background market risk as well as feedback contagion effects of the loss process are taken into account. Moreover, we show that any exogenous specification of the volatility and contagion parameters actually yields a unique consistent loss process and thus an arbitrage‐free family of ( T , x ) ‐bond prices. For the sake of analytical and computational efficiency we then develop a tractable class of doubly stochastic affine term structure models.