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Unifying Discrete Structural Credit Risk Models and Reduced-Form Models

by Cho-Jieh Chen of the University of Waterloo, and
Harry Panjer of the University of Waterloo

July 15, 2002

Summary: In a structural credit risk model, a default event is triggered by the capital structure when the value of the obligor falls below its financial obligation. In a reduced-form model, the bond price of a firm is considered as the current value under risk neutral valuation of a contingent claim paying full obligation (of one unit, say) if no default event happens and paying a fraction of promised payment or nothing if a default event happens. With model-specific assumptions, the bond price can be reduced to the mean of recovery rate and the probability of default for discrete models or an intensity process for continuous models. Based on no-arbitrage assumption, we show that the yield-spread formula for a reduced-form model is equivalent to a credit-spread formula for a structural model if the value of the firm follows a diffusion process or a jump-diffusion process. If the strong priority rule is applied, the prices of bonds of different seniority classes reflect the distribution function for the jump size and jump frequency. For reduced-form models, we shows that the forward credit spread for a RTV scheme can be given by a simple formula which converges to the credit spread for a RMV scheme.

Keywords: Default risk, Brownian motion, Jump-diffusion process, Structural model, Reduced-form model.

Published in: Insurance: Mathematics and Economics, Vol. 33, No. 2, (October 2003), pp. 357-380.

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