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Model Order Reduction for Parametric High Dimensional Models in the Analysis of Financial Risk = = Modellreduktion fur parametrische hochdimensionale Modelle bei der finanziellen Risikoanalyse.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Model Order Reduction for Parametric High Dimensional Models in the Analysis of Financial Risk =/
其他題名:	Modellreduktion fur parametrische hochdimensionale Modelle bei der finanziellen Risikoanalyse.
作者:	Jadhav, Onkar Sandip.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2022,
面頁冊數:	156 p.
附註:	Source: Dissertations Abstracts International, Volume: 84-01, Section: B.
Contained By:	Dissertations Abstracts International84-01B.
標題:	Monte Carlo simulation. -
ISBN:	9798835549399

Model Order Reduction for Parametric High Dimensional Models in the Analysis of Financial Risk = = Modellreduktion fur parametrische hochdimensionale Modelle bei der finanziellen Risikoanalyse.
Jadhav, Onkar Sandip.

Model Order Reduction for Parametric High Dimensional Models in the Analysis of Financial Risk =Modellreduktion fur parametrische hochdimensionale Modelle bei der finanziellen Risikoanalyse. - Ann Arbor : ProQuest Dissertations & Theses, 2022 - 156 p.

Source: Dissertations Abstracts International, Volume: 84-01, Section: B.

Thesis (M.Sc.)--Technische Universitaet Berlin (Germany), 2022.

This item must not be sold to any third party vendors.

Financial risk analysis is an excellent way of identifying and assessing the factors that may negatively affect investments. Investors use it to determine whether to undertake a particular investment, the plausible return and how to mitigate an activity's potential losses. However, the risk analysis of financial instruments often requires the valuation of such instruments under a wide range of future market scenarios, demanding efficient algorithms. In this thesis, the financial instruments are evaluated via the dynamics of short-rate models, based on the convection-diffusion-reaction partial differential equations (PDEs). These models are calibrated based on several thousand simulated yield curves that serve as market scenarios, which generate a high dimensional parameter space. In short, to perform the risk analysis, the financial model is needed to be solved for such a high dimensional parameter space, which requires efficient algorithms.Thus, this thesis presents a model order reduction (MOR) approach based on the proper orthogonal decomposition (POD) method to generate small model approximations for high dimensional parametric PDEs. The small model approximation called the reduced model is obtained by projecting the high dimensional model onto some reduced basis. The POD method relies on the method of snapshots in order to obtain the reduced basis. The snapshots are obtained by solving the full model generated by discretizing a PDE for some training parameters, which are further combined into a single matrix know as the snapshot matrix. Subsequently, the reduced basis is obtained by computing the truncated singular value decomposition (SVD) of the snapshot matrix.In this work, the training parameters are chosen based on greedy sampling approaches. We propose an adaptive greedy sampling approach that utilizes an optimized search based on surrogate modeling for the selection of the training parameter set. This approach avoids the cost of computing the error estimator for each parameter within the parameter space and instead uses a surrogate model to locate the training parameter set. The best suitable reduced model is procured such that the total error is less than the user-defined tolerance. The three significant numerical errors considered are the discretization error associated with the full model, the model order reduction error, and the parameter sampling error.This new technique is analyzed, implemented, and tested on industrial data of two financial instruments: A floater with caps and floors under the one-factor Hull-White model and a puttable steepener solved using the two-factor Hull-White model. The results illustrate that the reduced model approach works well for short-rate models and show potential applications in historical or Monte-Carlo value-at-risk calculations.

ISBN: 9798835549399Subjects--Topical Terms:

3564916
Monte Carlo simulation.

Model Order Reduction for Parametric High Dimensional Models in the Analysis of Financial Risk = = Modellreduktion fur parametrische hochdimensionale Modelle bei der finanziellen Risikoanalyse.
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245 1 0 $a Model Order Reduction for Parametric High Dimensional Models in the Analysis of Financial Risk = $b Modellreduktion fur parametrische hochdimensionale Modelle bei der finanziellen Risikoanalyse.
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500 $a Source: Dissertations Abstracts International, Volume: 84-01, Section: B.
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502 $a Thesis (M.Sc.)--Technische Universitaet Berlin (Germany), 2022.
506 $a This item must not be sold to any third party vendors.
520 $a Financial risk analysis is an excellent way of identifying and assessing the factors that may negatively affect investments. Investors use it to determine whether to undertake a particular investment, the plausible return and how to mitigate an activity's potential losses. However, the risk analysis of financial instruments often requires the valuation of such instruments under a wide range of future market scenarios, demanding efficient algorithms. In this thesis, the financial instruments are evaluated via the dynamics of short-rate models, based on the convection-diffusion-reaction partial differential equations (PDEs). These models are calibrated based on several thousand simulated yield curves that serve as market scenarios, which generate a high dimensional parameter space. In short, to perform the risk analysis, the financial model is needed to be solved for such a high dimensional parameter space, which requires efficient algorithms.Thus, this thesis presents a model order reduction (MOR) approach based on the proper orthogonal decomposition (POD) method to generate small model approximations for high dimensional parametric PDEs. The small model approximation called the reduced model is obtained by projecting the high dimensional model onto some reduced basis. The POD method relies on the method of snapshots in order to obtain the reduced basis. The snapshots are obtained by solving the full model generated by discretizing a PDE for some training parameters, which are further combined into a single matrix know as the snapshot matrix. Subsequently, the reduced basis is obtained by computing the truncated singular value decomposition (SVD) of the snapshot matrix.In this work, the training parameters are chosen based on greedy sampling approaches. We propose an adaptive greedy sampling approach that utilizes an optimized search based on surrogate modeling for the selection of the training parameter set. This approach avoids the cost of computing the error estimator for each parameter within the parameter space and instead uses a surrogate model to locate the training parameter set. The best suitable reduced model is procured such that the total error is less than the user-defined tolerance. The three significant numerical errors considered are the discretization error associated with the full model, the model order reduction error, and the parameter sampling error.This new technique is analyzed, implemented, and tested on industrial data of two financial instruments: A floater with caps and floors under the one-factor Hull-White model and a puttable steepener solved using the two-factor Hull-White model. The results illustrate that the reduced model approach works well for short-rate models and show potential applications in historical or Monte-Carlo value-at-risk calculations.
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