Modelling examples of loss given default and probability of default

Abstract

The Basel II accord regulates risk and capital management requirements to ensure that a bank holds enough capital proportional to the exposed risk of its lending practices. Under the advanced internal ratings based (IRB) approach, Basel II allows banks to develop their own empirical models based on historical data for probability of default (PD), loss given default (LGD) and exposure at default (EAD). This thesis looks at some examples of modelling LGD and PD.

One part of this thesis investigates modelling LGD for unsecured personal loans. LGD is estimated through estimating Recovery Rate (RR, RR=1-LGD). Firstly, the research examines whether it is better to estimate RR or Recovery Amounts. Linear regression and survival analysis models are built and compared when modelling RR and Recovery Amount, so as to predict LGD. Secondly, mixture distribution models are developed based on linear regression and survival analysis approaches. A comparison between single distribution models and mixture distribution models is made and their advantages and disadvantages are discussed.

Thirdly, it is examined whether short-term recovery information is helpful in modelling final RR. It is found that early payment patterns and short-term RR after default are very significant variables in final RR prediction models. Thus, two-stage models are built. In the stage-one model short-term Recoveries are predicted, and then the predicted short-term Recoveries are used in the final RR prediction models. Fourthly, macroeconomic variables are added in both the short-term Recoveries models and final RR models, and the influences of macroeconomic environment on estimating RR are looked at.

The other part of this thesis looks at PD modelling. One area where there is little literature of PD modelling is in invoice discounting, where a bank lends a company a proportion of the amount it has invoiced its customers in exchange for receiving the cash flow from these invoices. Default here means that the invoicing company defaults, at which point the bank cannot collect on the invoices. Like other small firms, the economic conditions affect the default risk of invoicing companies. The aim of this research is to develop estimates of default that incorporate the details of the firm, the current and past position concerning the invoices, and also economic variables.

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