A General Formula for Valuing Defaultable Securities

Previous research has shown that under a suitable no-jump condition, the price of a defaultable security is equal to its risk-neutral expected discounted cash flows if a modified discount rate is introduced to account for the possibility of default. Below, we generalize this result by demonstrating...

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Bibliographic Details
Published in:Econometrica 2004-09, Vol.72 (5), p.1377-1407
Main Authors: Collin-Dufresne, P., Goldstein, R., Hugonnier, J.
Format: Article
Language:English
Subjects:
absolutely continuous change of measures
Applications
Applied sciences
Conditional probabilities
counterparty risk
Credit risk
Default
Defaultable securities
Economic models
Economic theory
Exact sciences and technology
Financial instruments
Financial securities
Flight to quality
Insurance, economics, finance
Investors
Martingales
Mathematics
Operational research and scientific management
Operational research. Management science
Probability and statistics
Probability theory and stochastic processes
Probability theory on algebraic and topological structures
Risk theory. Actuarial science
risk-adjusted discounting
Sciences and techniques of general use
Securities
Security prices
Statistics
Stopping distances
Studies
Valuation
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Summary:Previous research has shown that under a suitable no-jump condition, the price of a defaultable security is equal to its risk-neutral expected discounted cash flows if a modified discount rate is introduced to account for the possibility of default. Below, we generalize this result by demonstrating that one can always value defaultable claims using expected risk-adjusted discounting provided that the expectation is taken under a slightly modified probability measure. This new probability measure puts zero probability on paths where default occurs prior to the maturity, and is thus only absolutely continuous with respect to the risk-neutral probability measure. After establishing the general result and discussing its relation with the existing literature, we investigate several examples for which the no-jump condition fails. Each example illustrates the power of our general formula by providing simple analytic solutions for the prices of defaultable securities.
ISSN:0012-9682
1468-0262
DOI:10.1111/j.1468-0262.2004.00538.x