Estimation of Tail-Related Value at Risk Measures: Range-Based Extreme Value Approach

Quantitative Finance (2014)

20 Pages Posted: 14 Jun 2013 Last revised: 14 Sep 2021

See all articles by Heng-Chih Chou

Heng-Chih Chou

National Taiwan Ocean University

David K. Wang

National University of Kaohsiung

Abstract

This study proposes a new approach for estimating value at risk (VaR). This approach combines quasi-maximum-likelihood fitting of asymmetric conditional autoregressive range (ACARR) models to estimate the current volatility and classical extreme value theory (EVT) to estimate the tail of the innovation distribution of the ACARR model. The proposed approach reflects two well-known phenomena found in most financial time series: stochastic volatility and the fat-tailedness of conditional distributions. This approach presents two main advantages over the McNeil and Frey (2000) approach. First, the ACARR model in this approach is an asymmetric model that treats the upward and downward movements of the asset price asymmetrically, whereas the generalized auto-regressive conditional hetero-skedasticity (GARCH) model in the McNeil and Frey (2000) approach is a symmetric model that ignores the asymmetric structure of the asset price. Second, the proposed method uses classical EVT to estimate the tail of the distribution of the residuals to avoid the threshold issue in the modern EVT model. Since the McNeil and Frey (2000) approach uses modern EVT, it may estimate the tail of the innovation distribution poorly. Back testing of historical time series data shows that our approach gives better VaR estimates than the McNeil and Frey (2000) approach.

Keywords: risk management, value at risk (VaR), asymmetric conditional autoregressive range (ACARR) model, extreme value theory (EVT)

JEL Classification: C22, C53

Suggested Citation

Chou, Heng-Chih and Wang, David K., Estimation of Tail-Related Value at Risk Measures: Range-Based Extreme Value Approach. Quantitative Finance (2014), Available at SSRN: https://ssrn.com/abstract=2278292

Heng-Chih Chou

National Taiwan Ocean University ( email )

2 Bei-Ning Road
Keelung, Taiwan 20224
Taiwan

David K. Wang (Contact Author)

National University of Kaohsiung ( email )

Kaohsiung, 811
Taiwan

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