Three Essays on Credit Risk Models and Their Bayesian Estimation
Kwon, Tae Yeon
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CitationKwon, Tae Yeon. 2012. Three Essays on Credit Risk Models and Their Bayesian Estimation. Doctoral dissertation, Harvard University.
AbstractThis dissertation consists of three essays on credit risk models and their Bayesian estimation. In each essay, defaults or default correlation models are built under one of two main streams. In our ﬁrst essay, sequential estimation on hidden asset value and model parameters estimation are implemented under the Black-Cox model. To capture short-term autocorrelation in the stock market, we assume that market noise follows a mean reverting process. For estimation, two Bayesian methods are applied in this essay: the particle ﬁlter algorithm for sequential estimation of asset value and the generalized Gibbs sampling method for model parameters estimation. The ﬁrst simulation study shows that sequential hidden asset value estimation using option price and equity price is more efﬁcient and accurate than estimation using only equity price. The second simulation study shows that by applying the generalized Gibbs sampling method, model parameters can be successfully estimated under the model setting that there is no closed-form solution. In an empirical analysis using eight companies, half of which are DowJones30 companies and the other half non-Dow Jones 30 companies, the stock market noise for the ﬁrms with more liquid stock is estimated as having smaller volatility in market noise processes. In our second essay, the frailty idea described in Dufﬁe, Eckner, Horel, and Saita (2009) is expanded to industry-speciﬁc terms. The MCEM algorithm is used to estimate parameters and random effect processes under the condition of unknown hidden paths and analytically-difﬁcult likelihood functions. The estimate used in the study are based on U.S. public ﬁrms between 1990 and 2008. By introducing industry-speciﬁc hidden factors and assuming that they are random effects, a comparison is made of the relative scale of within- and between-industries correlations. A comparison study is also developed among a without-hidden-factor model, a common-hiddenfactor model, and our industry-speciﬁc common-factor model. The empirical results show that an industry-speciﬁc common factor is necessary for adjusting over- or under-estimation of default probabilities and over- or under-estimation of observed common factor effects. Our third essay combines and extends works of the ﬁrst two essays by proposing a common model frame for both structural and intensity credit risk models. The common model frame combines the merits of several default correlation studies which are independently developed under each model setting. Following the work of Dufﬁe, Eckner, Horel, and Saita (2009), we apply not only observed common factors, but also un-observed hidden factor to explain the correlated defaults. Bayesian techniques are used for estimation and generalized Gibbs sampling and Metropolis-Hasting (MH) algorithms are developed. More than a simple combination of two model approaches (structural and intensity models), we relax the assumptions of equal factor effect across entire ﬁrms in previous studies, instead adopting a random coefﬁcients model. Also, a novelty of the approach lies in the fact that CDS and equity prices are used together for estimation. A simulation study shows that the posterior convergence is improved by adding CDS prices in estimation. Empirical results based on daily data of 125 companies comprising CDS.NA.IG13 in 2009 supports the necessity of such relaxations of assumption in previous studies. In order to demonstrate potential practical applications of the proposed framework, we derive the posterior distribution of CDX tranche prices. Our correlated structural model is successfully able to predict all the CDX tranche prices, but our correlated intensity model results suggests the need for further modiﬁcation of the model.
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