The normal inverse Gaussian distribution: exposition and applications to modeling asset, index and foreign exchange closing prices

Subject Applied Mathematics
Title The normal inverse Gaussian distribution: exposition and applications to modeling asset, index and foreign exchange closing prices
Author(s) Dean Teneng, Kalev Pärna
Keywords NIG distribution, modeling, index, asset, foreign exchange, goodness of fits tests
Abstract

We expose the unique properties of the normal inverse Gaussian distribution (NIG) useful for modeling asset, index and foreign exchange closing prices. We further demonstrate that traditional beliefs in asset, index, and foreign exchange closing prices not being independently identically distributed random variables are fundamentally flawed. Best models are selected using a novel model selection strategy proposed by Käärik and Umbleja (2011). Our results show that closing prices of Baltika and Ekpress Grupp (companies trading on Tallinn stock exchange), FTSE100, GSPC and STI (major world indexes), CHF/JPY, USD/EUR, EUR/GBP, SAR/CHF, QAR/CHF and EGP/CHF (Foreign Exchange rates) can be modeled by NIG distribution. This means their underlying stochastic properties can fully be captured by NIG; very useful for predicting price movements, pricing models, underwriting and trading derivatives etc.

Acknowledgment: Research supported by Estonian Science foundation grant number 8802 and Estonian Doctoral School in Mathematics and Statistics.

The normal inverse Gaussian distribution: exposition and applications to modelling asset, index and foreign exchange closing prices

Subject Applied Mathematics
Title The normal inverse Gaussian distribution: exposition and applications to modelling asset, index and foreign exchange closing prices
Author(s) Dean Teneng, Kalev Pärna
Keywords NIG distribution, modelling, index, asset, foreign exchange, goodness of fits tests
Abstract

We expose the unique properties of the normal inverse Gaussian distribution (NIG) useful for modelling asset, index and foreign exchange closing prices. We further demonstrate that traditional beliefs in asset, index, and foreign exchange closing prices not being independently identically distributed random variables are fundamentally flawed. Best models are selected using a novel model selection strategy proposed by K\"{a}\"{a}rik and Umbleja (2011). Our results show that closing prices of Baltika and Ekpress Grupp (companies trading on Tallinn stock exchange), FTSE100, GSPC and STI (major world indexes), CHF/JPY, USD/EUR, EUR/GBP, SAR/CHF, QAR/CHF and EGP/CHF (Foreign Exchange rates) can be modeled by NIG distribution. This means their underlying stochastic properties can fully be captured by NIG; very useful for predicting price movements, pricing models, underwriting and trading derivatives etc Acknowledgment: Research supported by Estonian Science foundation grant number 8802 and Estonian Doctoral School in Mathematics and Statistics.