PROPERTIES, ESTIMATION AND APPLICATION TO FINANCIAL DATA FOR GENERALIZED HYPERBOLIC DISTRIBUTION WHEN THE INDEX PARAMETER IS

2021 ◽  
Vol 71 (1) ◽  
pp. 55-84
Author(s):  
Calvin B. Mainaa
Keyword(s):  
Financial Data ◽  
Generalized Hyperbolic Distribution ◽  
Hyperbolic 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>

The weak tail dependence coefficient of the elliptical generalized hyperbolic distribution

Extremes ◽  
2011 ◽  
Vol 15 (2) ◽  
pp. 159-174 ◽  
Author(s):  
Stephan Schlueter ◽  
Matthias Fischer
Keyword(s):  
Tail Dependence ◽  
Generalized Hyperbolic Distribution ◽  
Hyperbolic Distribution ◽  
Tail Dependence Coefficient

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

scholarly journals The HS-SAS and GSH-SAS Distribution as Model for Unconditional and Conditional Return Distributions

2016 ◽  
Vol 42 (1) ◽  
Author(s):  
Matthias Fischer ◽  
Klaus Herrmann
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Quantile Function ◽  
Form Solution ◽  
Cumulative Distribution ◽  
Generalized Hyperbolic Distribution ◽  
Financial Return ◽  
Hyperbolic Distribution ◽  
Return Distributions ◽  
New Distribution

We introduce two new skewed and leptokurtic distributions derived from the hyperbolic secant distribution and from Vaughan (2002)’s generalized hyperbolic distribution by use of the sinh-arcsinh transformation introduced in Jones and Pewsey (2009). Properties of these new distribution are given. Their flexibility for modeling financial return data is comparable to that of their most advanced peers. Contrary to the latter for both distributions a closed-form solution for the density, cumulative distribution and quantile function can be given.

A THEORETICAL MODEL FOR PORTFOLIO OPTIMIZATION DURING CRISIS

2016 ◽  
Vol 78 (6-5) ◽  
Author(s):  
Colin Cheong Kiat Gan ◽  
Sudarso Kaderi Wiryono ◽  
Deddy Priatmodjo Koesrindartoto ◽  
Budhi Arta Surya
Keyword(s):  
Risk Factors ◽  
Theoretical Model ◽  
Portfolio Optimization ◽  
Risk Measures ◽  
Risk Measure ◽  
Expected Returns ◽  
Practical Application ◽  
Generalized Hyperbolic Distribution ◽  
Subprime Mortgage ◽  
Hyperbolic Distribution

The premise of this paper is providing a theoretical model for a novel way to portfolio optimization using generalized hyperbolic distribution during crisis with risk measures, expected shortfall and standard deviation. Getting good expected returns from investing in portfolio assets like stocks, bonds and currencies during crisis period chosen is harder where the risks cannot be diverted because of disruptive financial jolts i.e. sudden and unprecedented events like subprime mortgage crises in 2008. Multivariate generalized hyperbolic distribution on joint distribution of risk factors from stocks, bonds and currencies is used because it can simplify the risk factors calculation by allowing them to be linearized. The results show the premise is true. The contributions are discovering both the appropriate probability distribution and risk measure will determine whether the portfolio is optimal or not. The practical application will be taking care of the risk to take care of the profit.

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