scholarly journals Comparison of parameter estimation methods for normal inverse Gaussian distribution

2020 ◽  
Vol 27 (1) ◽  
pp. 97-108
Author(s):  
Jeongyoen Yoon ◽  
Jiyeon Kim ◽  
Seongjoo Song
Keyword(s):  
Parameter Estimation ◽  
Gaussian Distribution ◽  
Inverse Gaussian Distribution ◽  
Estimation Methods ◽  
Inverse Gaussian ◽  
Normal Inverse Gaussian Distribution ◽  
Parameter Estimation Methods ◽  
Normal Inverse Gaussian

scholarly journals Clustering with the multivariate normal inverse Gaussian distribution

2016 ◽  
Vol 93 ◽  
pp. 18-30 ◽  
Author(s):  
Adrian O’Hagan ◽  
Thomas Brendan Murphy ◽  
Isobel Claire Gormley ◽  
Paul D. McNicholas ◽  
Dimitris Karlis
Keyword(s):  
Gaussian Distribution ◽  
Inverse Gaussian Distribution ◽  
Inverse Gaussian ◽  
Multivariate Normal ◽  
Normal Inverse Gaussian Distribution ◽  
Normal Inverse Gaussian

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 THE NORMAL INVERSE GAUSSIAN DISTRIBUTION AND SPOT PRICE MODELLING IN ENERGY MARKETS

2004 ◽  
Vol 07 (02) ◽  
pp. 177-192 ◽  
Author(s):  
FRED ESPEN BENTH ◽  
JŪRATĖ ŠALTYTĖ-BENTH
Keyword(s):  
Brownian Motion ◽  
Gaussian Distribution ◽  
Market Price ◽  
Energy Markets ◽  
Inverse Gaussian Distribution ◽  
Spot Price ◽  
Inverse Gaussian ◽  
Statistical Point ◽  
Normal Inverse Gaussian Distribution ◽  
Normal Inverse Gaussian

We model spot prices in energy markets with exponential non-Gaussian Ornstein–Uhlenbeck processes. We generalize the classical geometric Brownian motion and Schwartz' mean-reversion model by introducing Lévy processes as the driving noise rather than Brownian motion. Instead of modelling the spot price dynamics as the solution of a stochastic differential equation with jumps, it is advantageous from a statistical point of view to model the price process directly. Imposing the normal inverse Gaussian distribution as the statistical model for the Lévy increments, we obtain a superior fit compared to the Gaussian model when applied to spot price data from the oil and gas markets. We also discuss the problem of pricing forwards and options and outline how to find the market price of risk in an incomplete market.

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