Estimating the Structural Credit Risk Model When Equity Prices Are Contaminated by Trading Noises

by Jin-Chuan Duan of the National University of Singapore & the University of Toronto, and
Andras Fulop of ESSEC Business School and CREST, France

July 2007

Abstract: The transformed-data maximum likelihood estimation (MLE) method for structural credit risk models developed by Duan (1994) is extended to account for the fact that observed equity prices may have been contaminated by trading noises. With the presence of trading noises, the likelihood function based on the observed equity prices can only be evaluated via some nonlinear filtering scheme. We devise a particle filtering algorithm that is practical for conducting the MLE estimation of the structural credit risk model of Merton [1974]. We implement the method on the Dow Jones 30 firms and on 100 randomly selected firms, and find that ignoring trading noises can lead to significantly over-estimating the firm's asset volatility. The estimated magnitude of trading noise is in line with the direction that a firm's liquidity will predict based on three common liquidity proxies. A simulation study is then conducted to ascertain the performance of the estimation method.

JEL Classification: C22.

Keywords: Particle filtering, maximum likelihood, option pricing, credit risk, microstructure.

Forthcoming in: Journal of Econometrics.

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