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Generalized hyperbolic processes autocovariance functions

Troush N. N., Kuzmina A.

Studia Informatica : systems and information technology

2014

Vol. 1-2(18)

37--45

Generalized hyperbolic processes are Levy processes which allow an almost perfect fit to financial data. Autocovariance functions of generalized hyperbolic processes such as the normal inverse Gaussian process, the variance gamma process and the hyperbolic process are deduced at this paper.

Option pricing by Esscher transforms in the cases of normal inverse Gaussian and variance gamma processes

Troush N. N., Kuzmina A. V.

Studia Informatica : systems and information technology

2012

Vol. 1-2(16)

35--43

The class of Esscher transforms is an important tool for option pricing Gerber and Shiu (1994) showed that the Esscher transform is an efficient technique for valuing derivative securities if the log returns of the underlying securities are governed by certain stochastic processes with stationary and independent increments. Levy processes are the processes of such type. Special cases of the Levy processes such as the normal inverse Gaussian process and the variance gamma process are considered at this paper. Values of these processes parameters for the existence of Esscher transform are deduced. A new algorithm of a normal inverse Gaussian process and variance gamma process simulation is also presented in this paper. These algorithm is universal and simpler one compared with analogous algorithms.