Credit Risk Modeling

Overview

Credit risk is the risk that a borrower will default on a loan. It is a significant risk for banks and other financial institutions.

The modeling of credit risk is very similar in structure to the modeling of an Insurance Policy Portfolio

Credit Risk Models

• Total Loss Time Series : the simplest way to model credit losses is to aggregate total losses by period and then to model it as a time series. This type of model can inform the modeler of the high level statistics (average loss and standard deviation)
• Credit Scoring : refers to the process of assigning a finite set of credit scores to a loan portfolio. For example, you could assign a numeric value of 1 to 5 to each loan, indicating its credit worthiness.
• Linear Discriminant :
• Pd, Lgd, Ead (Individual Risk) : The pd, lgd, ead framework consists of factoring average credit loss using the following definitions
  
  
  • PD - probability of default
  • LGD - loss given default. The percentage of the remaining value of the loan that the lender recoups.
  • EAD - exposure at default. This is the size of the remaining value of the loan at the time the default occurs. That is, the exposure is much less at the end of the loan than at the beginning.
• Td, Lgd, Ead - a variant of pd, lgd, ead, where pd is replaced by time to default.
• Transition Matrix : The transition matrix method models the credit quality of a loan in addition to default. It assigns a set of credit ratings to a loan and models the probability that a loan transitions from one rating to another, creating a model that can accomodate credit losses from write downs.
• Credit Spreads : infers the risk that the market is estimating for a fixed income instrument based on its spread to the risk free rate.

Credit Portfolio Models

Portfolio models are models that will model the credit risk of an entire portfolio, rather than just a single asset. Portfolio losses in general are not just the sum of the losses of a set of independent assets due to the correlations between assets.

• Portfolio from Individual Assets - Once the individual assets have been modeled, it is time to aggregate the results into a portfolio. For a credit portfolio, the portfolio cant be modeled as the sum of the results of each asset. This is due to the fact that the defaults and loss size for individual assets are often correlated, and this must be included explicitly in the model.
• Portfolio (Collective Model) - constructs a model of the number of portfolio defaults by modeling the portfolio as a whole, rather than as a sum of assets.

Credit Monte Carlo

Simulating Credit Risk - one of the primary methods of calculating total credit risk without using excessively simplistic assumptions.