The Implicit Estimation of Default Intensities and Recovery Rates

This article covers the implicit estimation of the parameters in the Jarrow/Turnbull (1995) default risk model. We demonstrate by means of a simulation analysis that joint estimation of the default intensity and the recovery rate by non-linear least squares is numerically unstable. Therefore, we suggest a stepwise estimation procedure. We fix the recovery rate and estimate the default intensity conditional on the recovery rate. This can be done for various recovery rates. We show that if data - either real world data or simulated data - does not deviate too much from the Jarrow/Turnbull model, the recovery rate can be estimated by an analysis of the pricing errors (observed prices vs. model prices) resulting from the alternative combinations of default intensities (estimated conditionally on the recovery rate) and recovery rates (). Applying this technique to German AA bank bond data shows that empirical bond prices deviate too much from the Jarrow/Turnbull model to apply our stepwise procedure. Insofar, the recovery rate cannot be estimated from market prices. Therefore, it has to be withdrawn from exogenous sources, such as estimates based on observed recoveries when defaults occur. Taking such values from related literature and conditionally on them estimating default intensities from market prices provides a method easy to implement