10credit - ACTSC 445: Asset-Liability Management Department...

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ACTSC 445: Asset-Liability Management Department of Statistics and Actuarial Science, University of Waterloo Unit 10 – Credit Risk References (recommended readings): Chap. 8 and 9 of Quantitative Risk Management Introduction Credit Risk is the risk that the value of a portfolio will change due to unexpected changes in the credit quality of issuers or trading partners Includes both losses due to defaults and losses caused by changes in credit quality of issuers Credit risk models are used for two main tasks: 1. Credit Risk Management: goal is to determine the loss distribution of a loan or bond portfolio over a Fxed-time period, compute risk measures and make risk-capital allocations 2. Analysis (mostly pricing) of credit-risky securities, such as credit-default swaps Categories of models static vs dynamic: static models are typically for credit risk management, while dynamic models or for pricing credit-risky securities structural (or Frm-value or threshold) vs reduced-form: structural models were initiated by Mer- ton in 1974; default occurs when a random variable (or process) falls below a threshold repre- senting the liabilities; in reduced-form models the precise mechanism leading to default is left unspeciFed; the default time of a Frm is modelled as a non-negative random variable whose distribution depends on a set of economic variables. Challenges of credit risk management 1. Lack of public information and data : makes it very hard to calibrate models, and also results in asymmetric information 2. Skewed loss ditributions (frequent small proFts and occasional large losses); makes it di±cult to model tail accurately; appropriate distributions tend to be harder to work with than, e.g., normal distribution 3. Dependence modelling : defaults events tend to happen simultaneously and this has a signiFcant impact on the tail of the credit loss distribution. Needs to be modelled correctly. 1
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Plan for this unit We’ll frst talk about structural models oF deFault, starting with the well-known Merton’s model and some extensions, including models based on credit migration. Then we’ll discuss threshold models, which can be viewed as a generalization oF Merton’s model. A useFul class oF models that are used to speciFy threshold models are copula-based models, so we’ll then introduce copulas and show how they can be used within threshold models. We’ll quickly discuss Li’s model and present some numerical results indicating the drawback oF this model, and conclude with a short discussion oF how some oF the Basel II regulations are related to these models. Structural Models of Default 1. Merton’s model Consider a frm whose asset value V t at time t is a random variable ⇒ { V t ,t 0 } is a stochastic process The asset value V t comes From two components: the frm’s equity and frm’s debt, whose values at time t are S t and B t , respectively. Hence we have V t = S t + B t , 0 t T . ±or the debt, we assume that the frm issues at time 0 a bond with Face value B
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This note was uploaded on 09/10/2010 for the course ACTSC 445 taught by Professor Christianelemieux during the Spring '09 term at Waterloo.

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10credit - ACTSC 445: Asset-Liability Management Department...

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