Alternative statistical distributions for estimating value-at-risk: theory and evidence

Lee, Cheng-Few; Su, Jung-Bin

doi:10.1007/s11156-011-0256-x

Cited by 25 publications

(10 citation statements)

References 26 publications

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“…To complicate matters, Lee and Su (2011) note that not only skewness but also the fat tails of the distribution are important in forecasting value at risk (VAR). Favre and Galeano (2002) propose adjustments to the Sharpe ratio to account for nonnormality in the return distribution through the use of the VAR methodology.…”

Section: <>mentioning

confidence: 99%

Term structure information and bond strategies

González

Skinner

Agyei-Ampomah

2012

Rev Quant Finan Acc

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We examine term structure theories by using a novel approach. We form bond investment strategies based on different theories of the term structure in order to determine which strategy performs best. When using a manipulation-proof performance measure, we find that consistent with prior literature, an active strategy that is based on time varying term premiums can indeed form the basis of a successful bond strategy that outperforms an unbiased expectation inspired passive bond buy and hold strategy. This is true, however, for an earlier time period when the literature first made this claim. In a later time period, we find that the passive buy and hold strategy is significantly superior to all active strategies. This result is confirmed by statistical tests and it suggests that once it became known that an active strategy based on time varying term premiums could outperform a passive buy and hold strategy, the markets adjusted and arbitraged away this opportunity. Overall, it appears that the unbiased expectation hypothesis is the most likely explanation of the behaviour of the term structure during more recent times. This is because economically and statistically significant superior performance cannot be achieved if one uses information from the forward curve or the term structure as a guide to adjusting bond portfolios in response to changes in the term premium.

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Section: <>mentioning

confidence: 99%

Term structure information and bond strategies

González

Skinner

Agyei-Ampomah

2012

Rev Quant Finan Acc

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“…In particular, the last two tables highlight how the most leptokurtic distribution, the GCHS, has a great advantage in estimating losses associated with high risk levels, thanks to a tail heaviness that is more pronounced relatively to the other GCLEs The out-of sample performance of the CGLE in estimating the value at risk was evaluated by using Kupiec's Likelihood Ratio test (LR;Kupiec 1995) and the Binomial Test (BT; Lee and Su 2012). Both the LR and BT null hypotheses state that the percentage of portfolio losses that in the second part of the sample exceed VaR α is equal to α.…”

Section: Evaluation Of Var and Es Via Gclesmentioning

confidence: 99%

Modeling Multivariate Financial Series and Computing Risk Measures via Gram–Charlier-Like Expansions

Zoia

Vacca

Barbieri

2020

Risks

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This paper develops an approach based on Gram–Charlier-like expansions for modeling financial series to take in due account features such as leptokurtosis. A Gram–Charlier-like expansion adjusts the moments of interest of a given distribution via its own orthogonal polynomials. This approach, formerly adopted for univariate series, is here extended to a multivariate context by means of spherical densities. Previous works proposed the Gram–Charlier of the multivariate Gaussian, obtained by using Hermite polynomials. This work shows how polynomial expansions of an entire class of spherical laws can be worked out with the aim of obtaining a wide set of leptokurtic multivariate distributions. A Gram–Charlier-like expansion is a distribution characterized by an additional parameter with respect to the parent spherical law. This parameter, which measures the increase in kurtosis due to the polynomial expansion, can be estimated so as to make the resulting distribution capable of describing the empirical kurtosis found in the data. An application of the Gram–Charlier-like expansions to a set of financial assets proves their effectiveness in modeling multivariate financial series and assessing risk measures, such as the value at risk and the expected shortfall.

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“…Note that if the return distribution is assumed to be Normal while it is not Normal, the true VaR is underestimated (Lee and Su 2012). The VaR computed for a longer time horizon, say L, is as follows:…”

Section: Var Measures and Their Validationmentioning

confidence: 99%

“…In the literature, Lee and Su (2012), among others, have recently shown that VaR estimates are sensitive to the return distribution assumption. Because we aim at comparing the volatility predictions of a set of models by means of VaR estimates, we should consider as a benchmark some VaR estimates robust to distribution misspecification.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of volatility predictions in a VaR framework

Amendola

Candila

2015

Quantitative Finance

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The evaluation of volatility forecasts is not straightforward and some issues can arise. A standard approach relies on statistical loss functions. Another approach bases the evaluation of the volatility predictions on utility functions or Value at Risk (VaR) measures. This work aims to combine the two approaches, using the VaR measures within the loss functions. By means of this method, the VaR measures obtained from a set of competing models are plugged into two loss functions, the magnitude loss function and a proposed new one. This latter loss function more heavily penalizes the models with a number of VaR violations greater than the expected one. The loss function values are evaluated against a benchmark obtained from the inclusion of a consistent estimate of the VaR measures in the loss function. In order to investigate the performance of the proposed method and the new loss function, aMonte Carlo experiment and an empirical analysis of a stock listed on the NewYork Stock Exchange are provided. The proposed strategy helps with the selection of a superior model, in terms of forecast accuracy, when the cited approaches do not clearly and uniquely identify it. Moreover, the new asymmetric loss function allows a greater discrimination with regard to models, helping to find the best volatility model

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Alternative statistical distributions for estimating value-at-risk: theory and evidence

Cited by 25 publications

References 26 publications

Term structure information and bond strategies

Term structure information and bond strategies

Modeling Multivariate Financial Series and Computing Risk Measures via Gram–Charlier-Like Expansions

Evaluation of volatility predictions in a VaR framework

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