Model Order Reduction for Finance

It is essential to be aware of the financial risk associated with an invested product. The risk analysis of financial instruments often requires the valuation of such instruments under a wide range of future market scenarios. The market scenarios (e.g., interest rates) are then input parameters in a valuation function that delivers the fair value of such financial instruments. These models are calibrated based on market scenarios that generate a high-dimensional parameter space. In short, to perform the risk analysis, the financial model needs to be solved for such a high dimensional parameter space, and this requires efficient algorithms. These two benchmark cases present the model order reduction approach based on the proper orthogonal decomposition approach with greedy sampling approaches for parameter sampling. The first case generates the 10000 simulated yield curves, which are then used to calibrate the financial model parameters. The second case presents both the classical and adaptive greedy sampling approaches.

In the source directory, one can find all source files required to run the benchmark cases. The directory benchmark contains the input data with the executable files. The Benchmark1_1.m file executes the yield curve simulation while the Benchmark1_2.nb file runs the parameter calibration. The classical greedy and adaptive greedy sampling techniques can be executed using Benchmark2_1.m and Benchmark2_2.m files. One can find a PDf file with a detailed step-by-step description of the benchmark case in the directory documentation.