Efficient VaR and Expected Shortfall computations for nonlinear portfolios within the delta-gamma approach

Luis Ortiz-Gracia; Cornelis W. Oosterlee

doi:10.1016/j.amc.2014.06.110

Efficient VaR and Expected Shortfall computations for nonlinear portfolios within the delta-gamma approach

Luis Ortiz-Gracia^*
, Cornelis W. Oosterlee

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We present four numerical methods to compute the Value-at-Risk and Expected Shortfall risk measure values of portfolios with financial options. The numerical methods are based on either wavelets or Fourier cosine approximations and belong to the class of Fourier inversion methods. We show that the risk measures can be efficiently calculated in terms of accuracy and CPU time. Besides, we provide a theoretical result about the shape of the resulting probability density. This a priori knowledge, allows us to enhance the efficiency and effectiveness of the proposed methods. Finally, we assess the accuracy of the approach in the presence of convexity or concavity properties of the financial portfolios.

Original language	English
Pages (from-to)	16-31
Number of pages	16
Journal	Applied Mathematics and Computation
Volume	244
DOIs	https://doi.org/10.1016/j.amc.2014.06.110
Publication status	Published - 1 Oct 2014
Externally published	Yes

Bibliographical note

Funding Information:
This work was carried out during the tenure of an ERCIM “Alain Bensoussan” Fellowship Programme. The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n o 246016.

Funding

This work was carried out during the tenure of an ERCIM “Alain Bensoussan” Fellowship Programme. The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n o 246016.

Keywords

Delta-gamma approximation
Expected Shortfall
Fourier transform
Haar wavelets
Market risk
Value-at-Risk

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10.1016/j.amc.2014.06.110

Cite this

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title = "Efficient VaR and Expected Shortfall computations for nonlinear portfolios within the delta-gamma approach",

abstract = "We present four numerical methods to compute the Value-at-Risk and Expected Shortfall risk measure values of portfolios with financial options. The numerical methods are based on either wavelets or Fourier cosine approximations and belong to the class of Fourier inversion methods. We show that the risk measures can be efficiently calculated in terms of accuracy and CPU time. Besides, we provide a theoretical result about the shape of the resulting probability density. This a priori knowledge, allows us to enhance the efficiency and effectiveness of the proposed methods. Finally, we assess the accuracy of the approach in the presence of convexity or concavity properties of the financial portfolios.",

keywords = "Delta-gamma approximation, Expected Shortfall, Fourier transform, Haar wavelets, Market risk, Value-at-Risk",

author = "Luis Ortiz-Gracia and Oosterlee, \{Cornelis W.\}",

note = "Funding Information: This work was carried out during the tenure of an ERCIM “Alain Bensoussan” Fellowship Programme. The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n o 246016.",

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AU - Ortiz-Gracia, Luis

AU - Oosterlee, Cornelis W.

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N2 - We present four numerical methods to compute the Value-at-Risk and Expected Shortfall risk measure values of portfolios with financial options. The numerical methods are based on either wavelets or Fourier cosine approximations and belong to the class of Fourier inversion methods. We show that the risk measures can be efficiently calculated in terms of accuracy and CPU time. Besides, we provide a theoretical result about the shape of the resulting probability density. This a priori knowledge, allows us to enhance the efficiency and effectiveness of the proposed methods. Finally, we assess the accuracy of the approach in the presence of convexity or concavity properties of the financial portfolios.

AB - We present four numerical methods to compute the Value-at-Risk and Expected Shortfall risk measure values of portfolios with financial options. The numerical methods are based on either wavelets or Fourier cosine approximations and belong to the class of Fourier inversion methods. We show that the risk measures can be efficiently calculated in terms of accuracy and CPU time. Besides, we provide a theoretical result about the shape of the resulting probability density. This a priori knowledge, allows us to enhance the efficiency and effectiveness of the proposed methods. Finally, we assess the accuracy of the approach in the presence of convexity or concavity properties of the financial portfolios.

KW - Delta-gamma approximation

KW - Expected Shortfall

KW - Fourier transform

KW - Haar wavelets

KW - Market risk

KW - Value-at-Risk

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DO - 10.1016/j.amc.2014.06.110

M3 - Article

AN - SCOPUS:84904788842

SN - 0096-3003

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SP - 16

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JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Efficient VaR and Expected Shortfall computations for nonlinear portfolios within the delta-gamma approach

Abstract

Bibliographical note

Funding

Keywords

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