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Calibration of Structural and Reduced-form Recovery Models

by Alexander F.R. Koivusalo of Danske Capital & the University of Duisburg-Essen, and
Rudi Schäfer of the University of Duisburg-Essen

February 23, 2011

Abstract: In recent years research on credit risk modelling has mainly focused on default probabilities. Recovery rates are usually modelled independently, quite often they are even assumed constant. Then, however, the structural connection between recovery rates and default probabilities is lost and the tails of the loss distribution can be underestimated considerably. The problem of underestimating tail losses becomes even more severe, when calibration issues are taken into account. To demonstrate this we choose a Merton-type structural model as our reference system. Diffusion and jump-diffusion are considered as underlying processes. We run Monte Carlo simulations of this model and calibrate different recovery models to the simulation data. For simplicity, we take the default probabilities directly from the simulation data. We compare a reduced-form model for recoveries with a constant recovery approach. In addition, we consider a functional dependence between recovery rates and default probabilities. This dependence can be derived analytically for the diffusion case. We find that the constant recovery approach drastically and systematically underestimates the tail of the loss distribution. The reduced-form recovery model shows better results, when all simulation data is used for calibration. However, if we restrict the simulation data used for calibration, the results for the reduced-form model deteriorate. We find the most reliable and stable results, when we make use of the functional dependence between recovery rates and default probabilities.

JEL Classification: C15, G21, G24, G28, G33.

Keywords: Credit risk, Loss distribution, Reduced-form models, Structural models, Value at Risk, Expected Tail Loss, Stochastic processes

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