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The sample period for our study is November 1, 1999 through July 31, 2002. Our choice of sample period was primarily driven by data considerations, i.e., our empirical analysis requires secondary market daily prices of loans, which were not available prior to November 1, 1999. The dataset we use is a unique dataset of daily secondary market loan prices from the Loan Syndications and Trading Association (LSTA) and Loan Pricing Corporation (LPC) mark-to-market pricing service, supplied to over 100 institutions managing over $200 billion in bank loan assets. This dataset consists of daily bid and ask price quotes aggregated across dealers. Each loan has a minimum of. | Modeling Term Structures of Defaultable Bonds Darrell Duffie Stanford University Kenneth J. Singleton Stanford University and NBER This article presents convenient reduced-form models of the valuation of contingent claims subject to default risk focusing on applications to the term structure of interest rates for corporate or sovereign bonds. Examples include the valuation of a credit-spread option. This article presents a new approach to modeling term structures of bonds and other contingent claims that are subject to default risk. As in previous reduced-form models we treat default as an unpredictable event governed by a hazard-rate process. 1 Our approach is distinguished by the parameterization of losses at default in terms of the fractional reduction in market value that occurs at default. Specifically we fix some contingent claim that in the event of no default pays X at time T. We take as given an arbitrage-free setting in which all securities are priced in terms of some short-rate process r and equivalent martingale measure Q see Harrison and Kreps 1979 and Harrison and Pliska 1981 . Under this risk-neutral probability measure we let ht denote the hazard rate for default at time t and let Lt denote the expected fractional loss in market value if default were to occur at time t conditional This article is a revised and extendedversion ofthe theoretical results from our earlier article Econometric Modeling of Term Structures of Defaultable Bonds June 1994 . The empirical results from that article also revised and extended are now found in An Econometric Model of the Term Structure of Interest Rate Swap Yields Journal of Finance October 1997 . We are grateful for comments from many including the anonymous referee Ravi Jagannathan the editor Peter Carr Ian Cooper Qiang Dai Ming Huang Farshid Jamshidian Joe Langsam Francis Longstaff Amir Sadr Craig Gustaffson Michael Boulware Arthur Mezhlumian and especially Dilip Madan. We are also grateful for financial .
