“If we tried to model the Change of Measure approach in C++, we’d have to write low-level code for manipulating matrices and statistical analysis. Instead, we wrote more concise MATLAB code and then compiled the MATLAB code into an Excel add-in, resulting in much faster development.”
Dr. Aniruddho Sanyal, Wolters Kluwer
New regulatory requirements and shareholder demands have increased the need for operational risk modeling and management. To safeguard against operational risk, many financial institutions have adopted the Change of Measure (COM) approach described in a groundbreaking paper by Kabir Dutta and David Babbel1. Several major U.S. banks have already committed resources to developing proprietary models of the COM approach, which combines internal loss data with scenario analysis to calculate a single, reliable estimate of operational risk capital.
Working in MATLAB®, analysts at Wolters Kluwer have developed the first implementation of the COM approach that enables financial institutions to apply COM without developing their own models.
“MATLAB and Statistics Toolbox enabled us to rapidly implement the COM methodology,” says Dr. Aniruddho Sanyal, senior consultant at Wolters Kluwer. “With MATLAB Builder EX we packaged our implementation as a Microsoft Excel add-in that our clients can access from within Excel to perform their own operational risk analyses.”
Basel II allows institutions to calculate operational risk using one of three approaches: basic indicator, standardized, or advanced measurement (AMA). The basic indicator and standardized approaches yield high capital estimates and make it difficult to perform scenario analysis and stress testing. Most smaller financial institutions, including banks in emerging markets, do not apply AMA, however, because they lack the resources to develop the advanced models required.
Wolters Kluwer sought to help these institutions by developing a packaged implementation of the COM approach that would incorporate the internal data, external data, and scenario analysis required by AMA.
The analysts needed a computational environment for performing parameter estimation, goodness-of-fit tests, and other statistical analyses. After implementing the COM approach, they needed a way to package the solution that would protect their intellectual property while making it easy for financial analysts to measure their own operational risk capital.
Wolters Kluwer used MATLAB and Statistics Toolbox™ to develop a model that implements the COM approach.
The first step in the COM approach is to identify a distribution that fits a given set of internal loss data. The team implemented this step in the model by using Statistics Toolbox to perform parameter estimation on lognormal, loglogistic, loggamma, and Weibull distributions.
To evaluate how well the distributions matched the data, they added Anderson-Darling, Kolmogorov-Smirnov, and chi-square goodness-of-fit tests to the model. They used quantile-quantile (QQ) plots to visualize the goodness-of-fit evaluations.
The next step in the COM approach is to incorporate scenario data, which is based on the actual loss experience of the financial institution. The team implemented this step in MATLAB by running 10,000 COM trials on each distribution and employing Statistics Toolbox to re-estimate distribution parameters using maximum-likelihood estimation.
The model uses the new distribution to estimate operational risk capital based on single loss approximation. For institutions with little or no historical loss data, the team implemented an alternative method that relies on an empirical distribution and Monte Carlo simulations in MATLAB to estimate capital.
Using MATLAB Compiler™ and MATLAB Builder™ EX, the team packaged the MATLAB model as a Microsoft® Excel add-in. Analysts at financial institutions can use this add-in directly within Excel to perform operational risk modeling, even if they do not have MATLAB installed.
As an alternative to this Excel interface, Wolters Kluwer plans to use MATLAB and Database Toolbox™ to implement a custom user interface that retrieves model inputs from, and stores the results in, a database.
Provide financial institutions with a quantitative solution for the measurement of operational risk capital
Use MATLAB and Statistics Toolbox to implement the Change of Measure approach for combining internal loss data with scenario analysis, and use MATLAB Builder EX to package the implementation as an Excel add-in