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

• Autorzy: Troush N. N. , Kuzmina A. V.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Esscher transforms; option pricing; generalized hyperbolic process; normal inverse Gaussian process; variance gamma process

• Wydawca: Wydawnictwo Uniwersytetu Przyrodniczo-Humanistycznego w Siedlcach
• Czasopismo: Studia Informatica : systems and information technology
• Rocznik: 2012
• Tom: Vol. 1-2(16)
• Strony: 35--43
• Opis fizyczny: Bibliogr. 9 poz., wykr.

Twórcy

autor

Troush N. N.

• Belarusian State University, Nezavisimosty pr., 4 Minsk, Republic of Belarus

autor

Kuzmina A. V.

• Belarusian State University, Nezavisimosty pr., 4 Minsk, Republic of Belarus

Bibliografia

• 1. Gerber H.U., Shiu E.S., 1994, Option pricing by Esscher transforms Transactions of society of actuaries, Vol. 46. 99-191.
• 2. Raible S., 2001, Levy processes in finance: theory, numerics, and empirical fact,. PhD thesis, Freiburg.
• 3. Barndorff-Nielsen O.E., 1998, Processes of normal inverse Gaussian type Finance Stochast. 2.41.
• 4. Madan D.B., Carr P.P., (ed.), 1998, The variance gamma process and option pricing. European Finance Preview, Vol. 2, 79-105.
• 5. Barndorff-Nielsen O.E., Halgreen C., 1997, Infinitely divisibility of the hyperbolic and generalized inverse Gaussian distributions, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete. Berlin, V 38, 309-311.
• 6. Cont R., Tankov P., 2003, Financial modeling with jump processes, Chapman and Hall CRC Press.
• 7. Schoutens W., 2003, Levy processes in finance / W. Schoutens. Bognor Regis: John Wiley & Sons Ltd.
• 8. Харин Ю.С., Малюгин В.И., 2008, Математические и компьютерные основы статистического анализа данных и моделирования, Минск: БГУ
• 9. Jorgensen B., 1982, Statistical properties of the generalized inverse Gaussian distribution, Berlin, V. 9, Springer.