Efficient Computation of Value at Risk with Heavy-Tailed Risk Factors

24 Pages Posted: 25 Aug 2009

See all articles by Cheng-der Fuh

Cheng-der Fuh

Academia Sinica

Inchi Hu

Hong Kong University of Science & Technology (HKUST) - Department of Information & Systems Management

Kate Hsu

University of Illinois at Urbana-Champaign

Ren-Her Wang

Department of Finance, National Taiwan University

Date Written: August 24, 2009

Abstract

The probabilities considered in value-at-risk (VaR) are typically of moderate deviations. However, the variance reduction techniques developed in the literature for VaR computation are based on large deviations methods. Modeling heavy-tailed risk factors using multivariate $t$ distributions, we develop a new moderate-deviations method for VaR computation. We show that the proposed method solves the corresponding optimization problem exactly, while previous methods produce approximations to the exact solution. Thus, the proposed method consistently outperforms existing methods derived from large deviations theory under various settings. The results are confirmed by a simulation study.

Keywords: Importance sampling, moderate deviation, multivariate t distribution, quadratic approximation, component VaR

JEL Classification: C15, C63, D30

Suggested Citation

Fuh, Cheng-der and Hu, Inchi and Hsu, Kate and Wang, Ren-Her, Efficient Computation of Value at Risk with Heavy-Tailed Risk Factors (August 24, 2009). 22nd Australasian Finance and Banking Conference 2009. Available at SSRN: https://ssrn.com/abstract=1460538 or http://dx.doi.org/10.2139/ssrn.1460538

Cheng-der Fuh

Academia Sinica ( email )

Nankang
Taipei, 11529
Taiwan

Inchi Hu

Hong Kong University of Science & Technology (HKUST) - Department of Information & Systems Management

Clear Water Bay, Kowloon
Hong Kong

Kate Hsu

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL 61820
United States

Ren-Her Wang (Contact Author)

Department of Finance, National Taiwan University ( email )

1 Sec. 4, Roosevelt Road
Taipei 106, 106
Taiwan

Register to save articles to
your library

Register

Paper statistics

Downloads
121
Abstract Views
872
rank
230,302
PlumX Metrics