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Fitting the variance-gamma model to financial data

Part of: Inference from stochastic processes Distribution theory - Probability Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Eugene Seneta
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Abstract

This paper has as its main theme the fitting in practice of the variance-gamma distribution, which allows for skewness, by moment methods. This fitting procedure allows for possible dependence of increments in log returns, while retaining their stationarity. It is intended as a step in a partial synthesis of some ideas of Madan, Carr and Chang (1998) and of Heyde (1999). Standard estimation and hypothesis-testing theory depends on a large sample of observations which are independently as well as identically distributed and consequently may give inappropriate conclusions in the presence of dependence.

Keywords

Variance-gammalog returnssubordinator modelskewnessincrementsdependencestationaritymethod of momentsestimationmartingalecharacteristic functiont-distribution’Student‘ processes

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60E07: Infinitely divisible distributions; stable distributions 62M05: Markov processes
Type
Part 3. Financial mathematics
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 177 - 187
Copyright
Copyright © Applied Probability Trust 2004 

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