Overview
The reduced form of operational risk models are models that do not try to model the causes of the risk. Rather, it tries to take a simple statistical approach to measuring the likelihood of the risk. This may involve measuring correlations with observed factors.
Simple Approach
The simplest reduced form approach just tries to estimate the moments of the distribution of operational risk from a dataset of observed losses due to that risk. For example, one may simply try to estimate the average and standard deviation of the loss due to operational risks.
As an example, the modeler could assume that the annual loss due to operational risk follows a lognormal distribution (because the loss cannot be less than zero, and has no upper bound). Then, using the method of moments simply fits the distribution to the measured mean and standard deviation of actual losses.
Factor Approach
The factor approach utitlizes a simple OLS regression to try to tie the magnitude of losses in a given year to a set of observable factors.
Compound Model
The compound model breaks operational risk into two models.
- Probability of Loss
- the first model is a model that indicates the probability of a loss event occurring in a given time frame, without specifying the size of the loss.
Probability of loss can be measured in many ways.
- As an average over a dataset where a 1 indicates a loss event and a 0 represents no loss event
- Using Logistic Regression to measure the probability of loss against a set of factors.
- Size of Loss - the second model models the size of the loss given that an event has occurred. This is done by assigning a distribution to the loss, (typically a lognormal or beta) and then fitting it with the method of moments.