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Parameter Estimation in Credit Models Under Incomplete Information

Journal article
Authors Alexander Herbertsson
Rüdiger Frey
Published in Communications in Statistics - Theory and Methods
Volume 43
Issue 7
Pages 1409-1436
ISSN 0361-0926
Publication year 2014
Published at Department of Economics
Pages 1409-1436
Language en
Keywords CDS index, Credit risk, Filtering, Maximum-likelihood
Subject categories Applied mathematics, Statistics, Mathematical statistics, Economics and Business


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.

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