scholarly journals Inverse Gaussian quadrature and finite normal-mixture approximation of the generalized hyperbolic distribution

2021 ◽  
Vol 388 ◽  
pp. 113302
Author(s):  
Jaehyuk Choi ◽  
Yeda Du ◽  
Qingshuo Song
Keyword(s):  
Gaussian Quadrature ◽  
Inverse Gaussian ◽  
Normal Mixture ◽  
Generalized Hyperbolic Distribution ◽  
Hyperbolic Distribution

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 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>

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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