Andreas Binder,
Onkar Jadhav,
Volker Mehrmann
S. 469 - 507
doi:
10.1553/etna_vol55s469
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol55s469
Abstract:
A parametric model order reduction (MOR) approach for simulating 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 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 for applications to the historical or Monte Carlo Value-at-Risk calculations.
financial risk analysis, short-rate models, convection-diffusion-reaction equation, finite element method, parametric model order reduction, proper orthogonal decomposition, adaptive greedy sampling, error analysis, packaged retail investment and insurance-based products
Published Online:
2022/05/16 12:27:57
Object Identifier:
0xc1aa5576 0x003d6f2c
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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