January 2015

Bayesian Estimation of Time-Changed Default Intensity Models

Michael B. Gordy and Pawel J. Szerszen


We estimate a reduced-form model of credit risk that incorporates stochastic volatility in default intensity via stochastic time-change. Our Bayesian MCMC estimation method overcomes nonlinearity in the measurement equation and state-dependent volatility in the state equation. We implement on firm-level time-series of CDS spreads, and find strong in-sample evidence of stochastic volatility in this market. Relative to the widely-used CIR model for the default intensity, we find that stochastic time-change offers modest benefit in fitting the cross-section of CDS spreads at each point in time, but very large improvements in fitting the time-series, i.e., in bringing agreement between the moments of the default intensity and the model-implied moments. Finally, we obtain model-implied out-of-sample density forecasts via auxiliary particle filter, and find that the time-changed model strongly outperforms the baseline CIR model.

Accessible materials (.zip)

Keywords: Bayesian estimation, CDS, CIR process, credit derivatives, MCMC, particle filter, stochastic time change

DOI: http://dx.doi.org/10.17016/FEDS.2015.002

PDF: Full Paper

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Last Update: June 19, 2020