I need some assistance with these assignment. the effects of estimation error on measures of portfolio credit risk Thank you in advance for the help! More precisely, I analyse the impact of uncertainty about input parameters on the precision of measures of portfolio risk. I confine the analysis to losses from the default, i.e., exclude the risk of credit quality changes, and model default correlations by means of correlated latent variables. The framework builds on CreditMetrics (JP Morgan, 1997), and closely resembles the one used by the Basel Committee on Banking Supervision (2001) to adjust capital requirements for concentration risks.
The necessary inputs for assessing default risk are default rates, recovery rates, and default correlations. They are usually derived from historical data, which means that their precision can be inferred using standard statistical methodology. This is the first step of the analysis in this paper. In the second, I determine the accuracy of value at risk (VaR) measures in the presence of noisy input parameters. This is done separately for portfolios which differ in their average credit quality and in diversification across obligors.
The aim of such an analysis is threefold. First, the results are useful for defining the role credit risk models should play in credit portfolio management and bank regulation. Second, modelling parameter uncertainty allows computing risk measures which take estimation error into account. Since the loss distribution is a non-linear function of the input parameters, its estimate can be biased even if the parameter estimates are not. To correct such biases, I employ a Bayesian approach and analyse the predictive distribution, which averages the loss distributions pertaining to different but possibly true parameter values. Finally, the analysis helps to identify inputs with a large marginal benefit of increasing input quality.
The analysis shows that estimation error in input parameters leads to considerable noise in estimated portfolio risk. The confidence bounds for risk measures are so wide that losses which are judged to occur with a probability of 0.3% may actually occur with a probability of 1%. Several observations, however, suggest that available credit risk models can be useful for risk management purposes even though their application is plagued with data problems. The magnitude of estimation error is comparable to a setting in which VaR estimates can be based on a long time series of portfolio losses, and it differs little between perfectly diversified portfolios and small portfolios with 50 obligors. In addition, the bias in conventional VaR figures which result from estimation error is modest. The relative importance of the three input factors for the quality of VaR estimates depends on the portfolio structure and the extremeness of the events under analysis. The impact of correlation uncertainty, for instance, is larger for more extreme events and for riskier portfolios. .
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