Tail asymptotics for the bivariate equi-skew generalized hyperbolic distribution and its Variance-Gamma special case

2021 ◽  
pp. 109182
Author(s):  
Thomas Fung ◽  
Eugene Seneta
Keyword(s):  
Tail Asymptotics ◽  
Generalized Hyperbolic Distribution ◽  
Hyperbolic Distribution ◽  
Variance Gamma ◽  
Special Case

scholarly journals A Variance Gamma model for Rugby Union matches

2020 ◽  
Vol 17 (1) ◽  
pp. 67-75
Author(s):  
John Fry ◽  
Oliver Smart ◽  
Jean-Philippe Serbera ◽  
Bernhard Klar
Keyword(s):  
Three Dimensional ◽  
Rugby Union ◽  
Three Dimensional Model ◽  
Gamma Model ◽  
Variance Gamma ◽  
Poisson Models ◽  
History Of ◽  
Bonus Points ◽  
Variance Gamma Model ◽  
Special Case

Abstract Amid much recent interest we discuss a Variance Gamma model for Rugby Union matches (applications to other sports are possible). Our model emerges as a special case of the recently introduced Gamma Difference distribution though there is a rich history of applied work using the Variance Gamma distribution – particularly in finance. Restricting to this special case adds analytical tractability and computational ease. Our three-dimensional model extends classical two-dimensional Poisson models for soccer. Analytical results are obtained for match outcomes, total score and the awarding of bonus points. Model calibration is demonstrated using historical results, bookmakers’ data and tournament simulations.

scholarly journals Consistency Bands for the Mean Excess Function and Application to Graphical Goodness-of-fit Test for Financial Data

2016 ◽  
Vol 8 (1) ◽  
pp. 42
Author(s):  
Amadou Diadie Ba ◽  
El Hadj Deme ◽  
Cheikh Tidiane Seck ◽  
Gane Samb Lo
Keyword(s):  
Goodness Of Fit ◽  
Empirical Processes ◽  
Financial Data ◽  
Generalized Hyperbolic Distribution ◽  
Goodness Of Fit Test ◽  
Excess Function ◽  
Monthly Data ◽  
Hyperbolic Distribution ◽  
Mean Excess Function ◽  
The Mean

<p>In this paper, we use the modern setting of functional empirical processes and recent techniques on uniform estimation for non parametric objects to derive consistency bands for the mean excess function in the i.i.d. case. We apply our results for modelling Dow Jones data to see how good the Generalized hyperbolic distribution fits monthly data.</p>

Pattern Search for Generalized Hyperbolic Distribution and Financial Risk Measure

2012 ◽  
Vol 155-156 ◽  
pp. 424-429
Author(s):  
Xiu Fang Chen ◽  
Gao Bo Chen
Keyword(s):  
At Risk ◽  
Gaussian Distribution ◽  
Risk Measure ◽  
Inverse Gaussian Distribution ◽  
Pattern Search ◽  
Inverse Gaussian ◽  
Generalized Hyperbolic Distribution ◽  
Hyperbolic Distribution ◽  
Normal Inverse Gaussian Distribution ◽  
Normal Inverse Gaussian

A new parameter estimation--- pattern search algorithm based on maximum likelihood estimation is used to estimate the parameters of generalized hyperbolic distribution, normal inverse Gaussian distribution and hyperbolic distribution, which are used to fit the log-return of Shanghai composite index. The goodness of fit is tested based on Anderson & Darling distance and FOF distance who pay more attention to tail distances of some distribution. Monte Carlo simulation are used to determin the critical values of Anderson & Darling distance and FOF distance of different distributions.Value at risk (VaR) and conditional value at risk (CVaR) are estimated for the fitted generalized hyperbolic distribution, normal inverse Gaussian distribution and hyperbolic distributio.The results show that generalized hyperbolic distribution family is more suitable for risk measure such as VaR and CVaR than normal distribution.

scholarly journals Uncertainty in Risk Modelling

2021 ◽  
Author(s):  
Harjas Singh
Keyword(s):  
Monte Carlo ◽  
Em Algorithm ◽  
Monte Carlo Simulations ◽  
Expectation Maximization ◽  
Value At Risk ◽  
Distribution Data ◽  
Generalized Hyperbolic Distribution ◽  
Risk Modelling ◽  
Underlying Distribution ◽  
Hyperbolic Distribution

In this thesis, we explore the uncertainty issues in risk modelling arising from the different approaches proposed in the literature and currently being used in the industry. The first type of methods that we discuss assume that the returns of the stocks follows a generalized hyperbolic distribution. Data is calibrated by the Expectation-Maximization (EM) algorithm in order to estimate the parameters in the underlying distribution. Once we have the parameters, we estimate the Value at Risk (VaR) and Expected Shortfall (ES) by using Monte Carlo simulations. Furthermore, we calibrate data to different copulas, including the Gauss Copula, the

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