**LGD Credit Risk Model: Estimation of capital with parameter uncertainty using MCMC**
by Xiaolin Luo of the CSIRO Mathematics, Informatics and Statistics, Sydney, and Pavel V. Shevchencko of the CSIRO Mathematics, Informatics and Statistics, Sydney November 23, 2010 **Abstract:** This paper investigates the impact of parameter uncertainty on capital estimate in the well-known extended Loss Given Default (LGD) model with systematic dependence between default and recovery. We demonstrate how the uncertainty can be quantified using the full posterior distribution of model parameters obtained from Bayesian inference via Markov chain Monte Carlo (MCMC). Results show that the parameter uncertainty and its impact on capital can be very significant. We have also quantified the effect of diversification for a finite number of borrowers in comparison with the infinitely granular portfolio.
**Keywords:** parameter uncertainty, probability of default, loss given default, economic capital, Markov chain Monte Carlo, Bayesian inference, credit risk
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