The ECM Procedure
Overview: ECM Procedure
The ECM procedure develops an economic capital model. A financial enterprise that incurs losses that are inherent to the nature of its business needs to estimate the extent of those losses across multiple business lines. Developing a model for the enterprise-wide losses enables such an enterprise not only to estimate the minimum capital it must set aside to cover the worst-case losses and meet regulatory requirements but also to assess the economic viability and improve the risk management abilities of the enterprise.
Although there is no one precise definition of economic capital, it is generally agreed that economic capital depends on the worst-case losses you expect to cover across your enterprise’s business lines or risk categories. The statistical approach that is described and illustrated in this chapter can be a component of an internal model that is allowed by a regulatory framework. Contrast the approach in this chapter to the standard model, which makes some fixed assumptions and is relatively easier to compute. However, the capital requirements that stem from using the standard model often overestimate the risks and result in higher capital requirements. So, it might be prudent to invest time and resources in developing an internal model to arrive at more accurate estimates of risk, which often result in lower capital requirements and enable you to free up some capital for developing your business and increasing shareholder value. The regulatory agency should be willing to accept your internal model as long as it is statistically sound and has reasonable assumptions.
For the purposes of the ECM procedure, a model for the total loss an enterprise can incur as a result of losses across its multiple lines of business is called an economic capital model (ECM). The process of estimating an ECM is called economic capital modeling. A particularly powerful method of developing an economic capital model consists of the following steps:
Collect the loss event data from all business lines that incur financial losses. The loss event data consist of frequency (count) of losses that a business line incurs in a particular time period and the severity (magnitude) of each loss.
Estimate separate loss distribution models for the frequency and severity for each business line. Usually, the frequency model is a parametric model that consists of a discrete probability distribution, and the severity model is a parametric model that consists of a continuous probability distribution. Each model can contain regression parameters that measure the impact of external factors on the location or shape of the probability distribution.
-
Create a compound distribution model (CDM) of the aggregate loss that a business line can incur in the particular time period. This step requires combining the frequency and severity models. Because of the possibly complex nature of the frequency and severity distributions, the CDM often cannot be encoded in a concise parametric form. Hence, it is usually estimated by simulating a large empirical sample of the aggregate loss.
At this step in the process, the worst-case losses for an individual business line can be estimated by computing the value-at-risk (VaR) or tail value-at-risk (TVaR) from the large empirical sample of the CDM.
Estimate a loss dependency structure of the losses across all business lines. This dependency structure essentially estimates how a loss in one business line is correlated with the losses in other business lines. A typical method of estimating the dependency is to fit a copula model to the aggregate losses in each business line, where losses are matched by the time period of interest.
Use the estimated dependency structure to simulate a large sample of probabilities of loss in all business lines. Each observation in the sample essentially records the probability of seeing a loss in each of the business lines in the time period of interest. In other words, each observation records one possible scenario where all business lines simultaneously incur losses, the extent of which varies according to the simulated probabilities. The simulated probabilities account for the dependency among the business lines. Simulating a large number of such scenarios provides a comprehensive picture of enterprise-wide losses. However, these simulation data are on the probability scale, which creates the need for the next step of the process.
For each observation in the copula simulation sample, invert the probability estimate of each business line by using that line’s aggregate loss sample, which the CDM simulation creates in the third step. This produces an estimate of the loss for each business line. Aggregating the losses across all business lines produces an estimate the total loss for that observation. Repeating this process for all the observations in the copula simulation table results in a large sample of the total loss, which essentially encodes the probability distribution model of the enterprise-wise losses.
Compute VaR and TVaR estimates for the total loss by using the large sample that the preceding step generates. These VaR and TVaR estimates help you decide the economic capital needs of your enterprise to cover worst-case losses and meet regulatory requirements.
SAS Econometrics offers various procedures to help you implement each modeling and simulation step of this process. The CNTSELECT and SEVSELECT procedures help you estimate a wide range of frequency and severity models, respectively. The CCDM procedure helps you estimate the compound distribution model (CDM) by simulating a large distributed sample of the aggregate loss for each business line. The CCOPULA procedure helps you fit and simulate various types of copula models.
The ECM procedure helps you implement the last two critical steps of the economic capital modeling process. It uses the large, distributed CDM samples to estimate the empirical distribution function (EDF) of each business line’s aggregate loss, and uses those EDF estimates to efficiently invert the probabilities in the large, distributed copula simulation sample.
The losses in each business line often depend on the economic and social environment in which the business operates. It is important to estimate the frequency and severity models that account for such external factors. The dependence of frequency and severity on external factors implies that the CDM and the economic capital model (ECM) also depend on those factors. Hence, it is not sufficient to estimate the ECM for just one set of values of the external factors, where each set of values is called an external scenario. You should estimate the ECM for multiple external scenarios, each representing a different possible state of the world. Because the CDM and ECM modeling steps need to be repeated for each external scenario, it is important that those steps run as efficiently as possible. Not only should each step use all available computational resources, but it should also be able to efficiently consume the data that the previous step generates. In particular, when the data are large and distributed across a cluster of computing and storage nodes, the modeling steps should consume the data in their distributed format instead of bringing them to one central node purely for the modeling purposes.
The SAS Econometrics procedures are designed to help you achieve computational efficiency, minimal data movement, and modeling convenience. The procedures other than PROC ECM are described in their respective chapters. This chapter describes the syntax and features of PROC ECM.
PROC ECM requires SAS Cloud Analytic Services (CAS) in order to run. Because PROC ECM runs on CAS, it also does the following:
enables you to run on a cluster of machines that distribute the data and the computations
exploits all the available cores and concurrent threads