Generalized Hyperbolic Distributions And Value-At-Risk Estimation For The South African Mining Index

Huang, Chun‐Kai; Chinhamu, Knowledge; Huang, Chun‐Sung; Hammujuddy, Jahvaid

doi:10.19030/iber.v13i2.8447

Cited by 11 publications

(9 citation statements)

References 18 publications

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“…Further work may include comparative analyses with other heavy-tail distributions, that are suitable for the depiction of financial returns, and incorporation of GPD in the framework of the well-known GARCH-based VaR models. For example, comparisons may be drawn with the generalised logistic distribution (Tolikas & Brown, 2006) and the class of generalised hyperbolic distributions (Huang et al, 2014), with the inclusion of backtesting results on the VaR and ES estimates. R and EViews were used in this paper to produce figures and results from various tests.…”

Section: Discussionmentioning

confidence: 99%

“…In contrast to VaR, ES measures the riskiness of an instrument by considering both the size and likelihood of losses above a particular threshold (Basel, 2012). ES gives the expected size of return that exceeds VaR, i.e., for a probability level p, (16) And, equivalently, (17) where the second term above represent the mean of the excess distribution (treating as the threshold). Proceeding as before, if the threshold is sufficiently large then is a GPD, i.e.,…”

Section: Esmentioning

confidence: 99%

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Extreme Risk, Value-At-Risk And Expected Shortfall In The Gold Market

Chinhamu¹,

Huang²,

Huang³

et al. 2014

IBER

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Extreme value theory (EVT) has been widely applied in fields such as hydrology and insurance. It is a tool used to reflect on probabilities associated with extreme, and thus rare, events. EVT is useful in modeling the impact of crashes or situations of extreme stress on investor portfolios. It describes the behavior of maxima or minima in a time series, i.e., tails of a distribution. In this paper, we propose the use of generalised Pareto distribution (GPD) to model extreme returns in the gold market. This method provides effective means of estimating tail risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). This is confirmed by various backtesting procedures. In particular, we utilize the Kupiec unconditional coverage test and the Christoffersen conditional coverage test for VaR backtesting, while the Bootstrap test is used for ES backtesting. The results indicate that GPD is superior to the traditional Gaussian and Students t models for VaR and ES estimations.

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Section: Discussionmentioning

confidence: 99%

Section: Esmentioning

confidence: 99%

Extreme Risk, Value-At-Risk And Expected Shortfall In The Gold Market

Chinhamu¹,

Huang²,

Huang³

et al. 2014

IBER

Self Cite

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show abstract

“…Through various perspectives, Fajardo, Farias and Ornelas recommended the use of the GH family distribution estimating by the maximum log likelihood method. Huang, et al (2014) applied the generalized hyperbolic distributions for VaR estimation for the South African mining index. Through the comparison of three subclasses of the generalized hyperbolic distributions using the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and log-likelihoods, Huang, et al found the generalized hyperbolic (GH) skew Student's t distribution as the most robust model for the South African mining index returns.…”

Section: Literature Reviewmentioning

confidence: 99%

Heavy-Tailed Distributions and Risk Management of Equity Market Tail Events

Guo¹

2017

SSRN Journal

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Traditional econometric modelling typically follows the idea that market returns follow a normal distribution. However, the concept of tail risk indicates that the distribution of returns is not normal, but skewed and has heavy tails. Thus, a heavy-tailed distribution, which accurately estimates the tail risk, would significantly improve quantitative risk management practice. In this paper, we compare four widely used heavy-tailed distributions using the S&P 500 daily returns. Our results indicate that the Skewed t distribution in Hansen (1994) has the superior empirical performance compared with the Student's t distribution, the normal reciprocal inverse Gaussian distribution and the generalized hyperbolic distribution. We further showed the Skewed t distribution could generate the VaR estimates closest to the nonparametric historical VaR estimates compared with other heavy-tailed distributions.

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“…Modelling these innovations has received a great interest among practitioners and parametric estimation of their distribution is conducted with distributions such as the Generalized Hyperbolic (GHYP) [6] and Skewed Exponential Power (SEPD) [7]- [8] distributions. Recently, Polynomial-Normal [9] and Polynomial-t-Student distributions [10] were used to fit the innovation of GARCH models for financial series.…”

Section: Introductionmentioning

confidence: 99%

A multimodal asymmetric exponential power distribution: Application to risk measurement for financial high-frequency data

Thibault¹,

Bondon²

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Interest in risk measurement for high-frequency data has increased since the volume of high-frequency trading stepped up over the two last decades. This paper proposes a multimodal extension of the Exponential Power Distribution (EPD), called the Multimodal Asymmetric Exponential Power Distribution (MAEPD). We derive moments and we propose a convenient stochastic representation of the MAEPD. We establish consistency, asymptotic normality and efficiency of the maximum likelihood estimators (MLE). An application to risk measurement for high-frequency data is presented. An autoregressive moving average multiplicative component generalized autoregressive conditional heteroskedastic (ARMA-mcsGARCH) model is fitted to Financial Times Stock Exchange (FTSE) 100 intraday returns. Performances for Value-at-Risk (VaR) and Expected Shortfall (ES) estimation are evaluated. We show that the MAEPD outperforms commonly used distributions in risk measurement.

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Generalized Hyperbolic Distributions And Value-At-Risk Estimation For The South African Mining Index

Cited by 11 publications

References 18 publications

Extreme Risk, Value-At-Risk And Expected Shortfall In The Gold Market

Extreme Risk, Value-At-Risk And Expected Shortfall In The Gold Market

Heavy-Tailed Distributions and Risk Management of Equity Market Tail Events

A multimodal asymmetric exponential power distribution: Application to risk measurement for financial high-frequency data

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