Error Analysis of a Model Order Reduction Framework for Financial Risk Analysis

TL;DR

This paper presents an adaptive parametric model order reduction method using POD for efficient and accurate financial risk simulations, significantly speeding up computations while maintaining precision.

Contribution

It introduces an adaptive greedy sampling approach for optimal reduced basis generation in financial PDE models, improving efficiency and accuracy over traditional methods.

Findings

Significant computational speedup achieved.

High accuracy maintained with reduced models.

Effective application demonstrated on industrial financial data.

Abstract

A parametric model order reduction (MOR) approach for simulating the high dimensional models arising in financial risk analysis is proposed on the basis of the proper orthogonal decomposition (POD) approach to generate small model approximations for the high dimensional parametric convection-diffusion reaction partial differential equations (PDE). The proposed technique uses an adaptive greedy sampling approach based on surrogate modeling to efficiently locate the most relevant training parameters, thus generating the optimal reduced basis. The best suitable reduced model is procured such that the total error is less than a user-defined tolerance. The three major errors considered are the discretization error associated with the full model obtained by discretizing the PDE, the model order reduction error, and the parameter sampling error. The developed technique is analyzed, implemented, and tested on industrial data of a puttable steepener under the two-factor Hull-White model. The results illustrate that the reduced model provides a significant speedup with excellent accuracy over a full model approach, demonstrating its potential applications in the historical or Monte Carlo value at risk calculations.