Model order reduction for the simulation of parametric interest rate models in financial risk analysis

Abstract

This paper presents a model order reduction approach for large scale high dimensional parametric models arising in the analysis of financial risk. To understand the risks associated with a financial product, one has to perform several thousand computationally demanding simulations of the model which require efficient algorithms. We establish a model reduction approach based on a variant of the proper orthogonal decomposition method to generate small model approximations for the high dimensional parametric convection-diffusion-reaction partial differential equations. This approach requires to solve the full model at some selected parameter values to generate a reduced basis. We propose an adaptive greedy sampling technique based on surrogate modeling for the selection of the sample parameter set. The new technique is analyzed, implemented, and tested on industrial data of a floater with cap and floor under the Hull–White model. The results illustrate that the reduced model approach works well for short-rate models.

Error analysis of a model order reduction framework for financial risk analysis

“…Thus, in a previous paper [7], we have established a parametric model order reduction (MOR) approach based on a variant of the proper orthogonal decomposition approach, which significantly reduces the overall computation time [6,13]. This MOR approach is computationally feasible [23] as it determines low-dimensional linear (or affine) subspaces [44,57] via a truncated singular value decomposition (SVD) of a snapshot matrix [53] that is computed by simulating the full model obtained by discretizing the PDE for a small number of pre-selected training parameter values.…”

“…The question of how to select these parameters is often the most challenging part of the process. Our previous work [7] has established greedy algorithms to determine the training parameters more efficiently. The adaptive greedy approach searches the entire parameter space efficiently using a surrogate model and determines the best suitable training parameters.…”

“…In a previous paper, we have considered a numerical example of a floater with caps and floors under the one-factor Hull-White model [7]. However, there are more complicated instruments, e.g., steepeners whose coupons depend on the difference between the two interest rates [1].…”

“…A detailed procedure for the yield curve simulation and the calibration of θ(t) based on simulated yield curves is described in [7,38], respectively. We have applied a finite element method to solve the PDE (2.1) numerically; for more details see [1].…”

The Promotion and Optimization of Bank Financial Products Using Consumers’ Psychological Perception

“…In the technology acceptance model, perceived convenience is proposed. It is defined as that compared with the traditional way of selecting bank financial products, the purchase process is simple and consumers are willing to understand ( Binder et al, 2021 ). Consumers can understand various information about financial products through the network platform.…”