Advanced IRB - Some Formulae in Internal-ratings-based Approach

Some Formulae in Internal-ratings-based Approach

Some credit assessments in standardised approach refer to unrated assessment. Basel II also encourages banks to initiate internal-ratings based approach for measuring credit risks. Banks are expected to be more capable of adopting more sophisticated techniques in credit risk management.

Banks can determine their own estimation for some components of risk measure: the probability of default (PD), loss given default (LGD), exposure at default (EAD) and effective maturity (M). For public companies, default probabilities are commonly estimated using either the structural model of credit risk proposed by Robert Merton (1974) or reduced form models like the Jarrow-Turnbull model. For retail and unlisted company exposures, default probabilities are estimated using credit scoring or logistic regression, both of which are closely linked to the reduced form approach. The goal is to define risk weights by determining the cut-off points between and within areas of the expected loss (EL) and the unexpected loss (UL), where the regulatory capital should be held, in the probability of default. Then, the risk weights for individual exposures are calculated based on the function provided by Basel II.

Below are the formulae for some banks’ major products: corporate, small-medium enterprise (SME), residential mortgage and qualifying revolving retail exposure. (S being Min(Max(Sales Turnover),5),50 )

In the formulas below,

• N(x) denotes the normal cumulative distribution function
• G(z) denotes the inverse cummulative distribution function
• PD is the probability of default
• LGD is the loss given default
• EAD is the exposure at default
• M is the effective maturity