Parameter Estimation in Credit Models Under Incomplete Information

Abstract

We consider the filtering model of Frey and Schmidt (2012) stated under the real probability measure and develop a method for estimating the parameters in this framework by using time-series data of CDS index spreads and classical maximum-likelihood algorithms. The estimation-approach incorporates the Kushner-Stratonovich SDE for the dynamics of the filtering probabilities. The convenient formula for the survival probability is a prerequisite for our estimation algorithm. We apply the developed maximum-likelihood algorithms on market data for historical CDS index spreads (iTraxx Europe Main Series) in order to estimate the parameters in the nonlinear filtering model for an exchangeable credit portfolio. Several such estimations are performed as well as accompanying statistical and numerical computations.

Keywords:

• CDS index
• Credit risk
• Filtering
• Maximum-likelihood

Mathematics Subject Classification:

• Primary 62F10
• Secondary 91B70, 60J27, 91B28

Acknowledgment

The authors would like to thank an anonymous reviewer for very useful comments and remarks.

Notes

Colors versions of one or more of the figures in the article can be found online at www.tandfonline.com/lsta.