Value at Risk When Daily Changes in Market Variables are not Normally Distributed

Hull, John C.; White, Alan

doi:10.3905/jod.1998.407998

Cited by 215 publications

(105 citation statements)

References 6 publications

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“…This is because, although we have a well defined distribution function in a closed form, using maximum likelihood techniques for parameter estimation leads to convergence issues (Hamilton, [16] [17]). Alternate methods have been suggested, such as fractile-to-fractile comparisons (Hull and White, [18]) and Bayesian updating schemes (Zangari,[19]). This paper uses the fractile ot be a solution at all -to-fractile comparison techni 2.5.…”

Section: Mixture Of Normal Distributions O Model Fat-mentioning

confidence: 99%

A Comparison of VaR Estimation Procedures for Leptokurtic Equity Index Returns

Bhattacharyya¹,

R²

2012

JMF

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The paper presents and tests Dynamic Value at Risk (VaR) estimation procedures for equity index returns. Volatility clustering and leptokurtosis are well-documented characteristics of such time series. An ARMA (1, 1)-GARCH (1, 1) approach models the inherent autocorrelation and dynamic volatility. Fat-tailed behavior is modeled in two ways. In the first approach, the ARMA-GARCH process is run assuming alternatively that the standardized residuals are distributed with Pearson Type IV, Johnson S U , Manly's exponential transformation, normal and t-distributions. In the second approach, the ARMA-GARCH process is run with the pseudo-normal assumption, the parameters calculated with the pseudo maximum likelihood procedure, and the standardized residuals are later alternatively modeled with Mixture of Normal distributions, Extreme Value Theory and other power transformations such as John-Draper, Bickel-Doksum, Manly, Yeo-Johnson and certain combinations of the above. The first approach yields five models, and the second approach yields nine. These are tested with six equity index return time series using rolling windows. These models are compared by computing the 99%, 97.5% and 95% VaR violations and contrasting them with the expected number of violations.

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Section: Mixture Of Normal Distributions O Model Fat-mentioning

confidence: 99%

A Comparison of VaR Estimation Procedures for Leptokurtic Equity Index Returns

Bhattacharyya¹,

R²

2012

JMF

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“…Therefore, the calculation based on the normal distribution assumption may underestimate the risk. Hull & White (1998) and Guermat & Harris (2001) use non-normal distributions and resolve the problem of fat tail.…”

Section: Literature Reviewmentioning

confidence: 99%

Does the VaR Measurement Using Monte-Carlo Simulation Work in China?—Evidence from Chinese Listed Banks

Wang¹,

Song²,

Lin³

2017

JFRM

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There are usually great demands for risk control in the banking industry. Value at risk (VaR) is an important risk measurement in the Basel Accords, and Monte-Carlo simulation is a common method for VaR measurement. We conduct a series of Monte-Carlo simulation for VaR measurement based on the banks listed in the China stock market. Our study thinks that it is reliable to use Monte-Carlo simulation to measure VaR in Chinese banks. Therefore, we think that such VaR measurement works in China.

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“…Given the overwhelming evidence of violations of normality, there have been a plethora of theoretical and empirical studies focusing on the impact of nonnormality of security prices on various issues such as value-at-risk calculations, option pricing, cross-sectional variation of stock returns, hedging decisions, etc. See, for example, Kraus and Litzenberger (1976), Hull and White (1998), Siddique (1999, 2000), Bakshi, Kapadia and Madan (2003), Carr and Wu (2007), and Gilbert, Jones and Morris (2006). This paper studies the effect of nonnormality on exchange options.…”

Section: Introductionmentioning

confidence: 99%

The impact of return nonnormality on exchange options

2008

Journal of Futures Markets

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The Margrabe formula is used extensively by theorists and practitioners not only on exchange options, but also on executive compensation schemes, real options, weather and commodity derivatives, etc. However, the crucial assumption of a bivariate normal distribution is not fully satisfied in almost all applications. The impact of nonnormality on exchange options is studied by using a bivariate Gram-Charlier approximation. For near-the-money exchange options, skewness and coskewness induce price corrections which are linear in moneyness, while kurtosis and cokurtosis induce quadratic price corrections. The nonnormality helps to explain the implied correlation smile observed in practice.

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Value at Risk When Daily Changes in Market Variables are not Normally Distributed

Cited by 215 publications

References 6 publications

A Comparison of VaR Estimation Procedures for Leptokurtic Equity Index Returns

A Comparison of VaR Estimation Procedures for Leptokurtic Equity Index Returns

Does the VaR Measurement Using Monte-Carlo Simulation Work in China?—Evidence from Chinese Listed Banks

The impact of return nonnormality on exchange options

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