Working Paper

Bayesian Estimation of Time-Changed Default Intensity Models

Abstract: 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.

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

JEL Classification: C11; C15; C58; G12; G17;

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Bibliographic Information

Provider: Board of Governors of the Federal Reserve System (U.S.)

Part of Series: Finance and Economics Discussion Series

Publication Date: 2015-01-06

Number: 2015-2

Pages: 47 pages