publication . Preprint . Other literature type . 2020

Model order reduction for parametric high dimensional models in the analysis of financial risk

Binder, Andreas; Jadhav, Onkar; Mehrmann, Volker;
Open Access English
  • Published: 27 Feb 2020
Abstract
Comment: 39 pages, 10 figures
Subjects
free text keywords: Financial risk analysis, short-rate models, convection-diffusion reaction equation, finite differencemethod, parametric model order reduction, proper orthogonal decomposition, adaptive greedy sampling, Packaged retail investment and insurance-based products (PRIIPs)., Quantitative Finance - Computational Finance, Mathematics - Numerical Analysis, 35L10, 65M06, 91G30, 91G60, 91G80
Funded by
EC| ROMSOC
Project
ROMSOC
Reduced Order Modelling, Simulation and Optimization of Coupled systems
  • Funder: European Commission (EC)
  • Project Code: 765374
  • Funding stream: H2020 | MSCA-ITN-EID
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Preprint . 2020
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Other literature type . 2020
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Zenodo
Other literature type . 2020
Provider: Datacite
50 references, page 1 of 4

2. Model Hierarchy 3 2.1. Bank Account and Short-Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2. Vasicek and Cox-Ingersoll-Ross Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3. Hull-White Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3. Yield Curve Simulation and Parameter Calibration 7 3.1. Yield Curve Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2. Parameter Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4. Numerical Methods 12 4.1. Finite Difference Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2. Parametric Model Order Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.3. Greedy Sampling Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.4. Adaptive Greedy Sampling Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5. Numerical Example 26 5.1. Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.2. Finite Difference Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.3. Model Order Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.4. Computational cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

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