CAMRADATA standardized on MATLAB® and companion toolboxes to develop applications that use copulas to model complex dependencies. Using the t-copula in MATLAB as a starting point, CAMRADATA developed more advanced models that incorporate conditional and asymmetric copulas.
They relied on MATLAB for matrix and vector computations throughout the project. “The MATLAB programming language lends itself very nicely to the language of risk,” says Dorey. “The way you write the math out on a piece of paper as vector matrix calculations translates identically to a line of MATLAB code.”
Using Statistics and Machine Learning Toolbox™, the researchers developed a factor analysis model that shows financial analysts how asset classes are linked through exposure to common factors, such as inflation or the price of oil.
Once they had added asymmetry and tail dependency to the basic correlation parameters, the team used Symbolic Math Toolbox™ to solve maximum likelihood problems and calibrate their models to existing data.
CAMRADATA researchers used MATLAB, Financial Toolbox™, and Optimization Toolbox™ to link and optimize behavioral finance and higher-moments risk budgeting models.
Global Optimization Toolbox and Financial Toolbox were used to develop defensive portfolio designs incorporating option payoff profiles on assets and liabilities. These structured solutions examine the value of using puts and calls to map assets onto liabilities.
For each model, CAMRADATA used MATLAB to build an interface that enables analysts to visualize results and interact with the model using an embedded Microsoft® Excel® spreadsheet.
Using Datafeed Toolbox™, the team gathers time series data from financial data providers such as Bloomberg and has the capability to link to Thomson Reuters Datastream.
CAMRADATA researchers have also used MathWorks tools to develop a universal copula, which enables them to model any seemingly intractable multidimensional relationship. The universal copula has a wide variety of applications, from 3D animation to machine cognition.