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Term structure modelling of defaultable bonds

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  • Schonbucher, Philipp

Abstract

In this paper we present a model of the development of the term structure of defaultable interest rates that is based on a multiple-defaults model. Instead of modelling a cash payoff in default we assume that defaulted debt is restructured and continues to be traded. The model allows for loss quotas that are not predictable while maintaining a very close link to the modelling of default-free interest rate modelling. We use the Heath-Jarrow-Morton (HJM) [21] approach to represent the terms structure of defaultable bond prices in terms of forward rates and concentrate on modelling the development of the term structure of the defaultable bonds and give conditions under which these dynamics are arbitrage-free. These conditions are a drift restriction that is closely related to the HJM drift restriction for risk-free bonds, and the restriction that the defaultable short rate must always be not below the risk-free short rate. By keeping the mechanism that triggers the defaults as general as possible, it is shown that the HJM-drift conditions must also be satisfied by bond prices derived from firm's value models with predictable times of default, and not only by bond prices derived from intensity based models. In its most general version the model is set in a marked point process framework, to allow for jumps in the defaultable rates at times of default.

Suggested Citation

  • Schonbucher, Philipp, 1997. "Term structure modelling of defaultable bonds," LSE Research Online Documents on Economics 119168, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:119168
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    File URL: http://eprints.lse.ac.uk/119168/
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    References listed on IDEAS

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    More about this item

    Keywords

    arbitrage; term structure of interest rates; default risk;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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