Approximation of Distribution of Log-returns with Normal Inverse Gaussian Process

2018 ◽  
Author(s):  
Oskars Rubenis ◽  
Andrejs Matvejevs
Keyword(s):  
Gaussian Process ◽  
Inverse Gaussian ◽  
Inverse Gaussian Process ◽  
Normal Inverse Gaussian

scholarly journals Increments of Normal Inverse Gaussian Process as Logarithmic Returns of Stock Price

2018 ◽  
Vol 21 ◽  
pp. 93-97
Author(s):  
Oskars Rubenis ◽  
Andrejs Matvejevs
Keyword(s):  
Gaussian Process ◽  
Normal Distribution ◽  
Stock Prices ◽  
Stock Price ◽  
High Accuracy ◽  
Price Dynamics ◽  
Inverse Gaussian ◽  
Inverse Gaussian Process ◽  
Normal Inverse Gaussian ◽  
New Distribution

Normal inverse Gaussian (NIG) distribution is quite a new distribution introduced in 1997. This is distribution, which describes evolution of NIG process. It appears that in many cases NIG distribution describes log-returns of stock prices with a high accuracy. Unlike normal distribution, it has higher kurtosis, which is necessary to fit many historical returns. This gives the opportunity to construct precise algorithms for hedging risks of options. The aim of the present research is to evaluate how well NIG distribution can reproduce stock price dynamics and to illuminate future fields of application.

scholarly journals Lévy Processes in Gold Option Modeling

2020 ◽  
Vol 12 (2) ◽  
pp. 65
Author(s):  
Sandya N. Kumari
Keyword(s):  
Gaussian Process ◽  
Futures Contracts ◽  
Future Price ◽  
Mathematical Framework ◽  
Inverse Gaussian ◽  
Variance Gamma Process ◽  
Inverse Gaussian Process ◽  
Gold Futures ◽  
Generalized Inverse Gaussian ◽  
Normal Inverse Gaussian

To price and hedge derivative securities, it is crucial to have a good model of the probability distribution of the underlying product. In financial markets under uncertainty, the classical Black-Scholes model cannot explain the empirical facts. To overcome this drawback, the Lévy process was introduced to financial modeling. Today Gold futures markets are highly volatile. The purpose of this paper is to develop a mathematical framework in which American options on Gold futures contracts are priced more effectively. In this work, the Generalized Hyperbolic process, Normal Inverse Gaussian Process, Generalized Inverse Gaussian Process and Variance Gamma Process were used to model the future price. Then, option prices under the risk-neutral pricing process were calibrated and then authors attempt to infer the density forecast of future Gold prices at a given time horizon. Finally, Normal Inverse Gaussian was selected as the best model for Gold options by significant quantitative comparison between parsimonious models.

Inverse Gaussian process models for degradation analysis: A Bayesian perspective

2014 ◽  
Vol 130 ◽  
pp. 175-189 ◽  
Author(s):  
Weiwen Peng ◽  
Yan-Feng Li ◽  
Yuan-Jian Yang ◽  
Hong-Zhong Huang ◽  
Ming J. Zuo
Keyword(s):  
Gaussian Process ◽  
Process Models ◽  
Inverse Gaussian ◽  
Inverse Gaussian Process ◽  
Degradation Analysis ◽  
Gaussian Process Models
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