|
Scaling Of Student T-Distribution And Properties Of Lévy-Student Processes
[Full Text]
AUTHOR(S)
K.W.S.N. Kumari
KEYWORDS
Student T-distribution, Lévy processes, Heavy-tailed distribution, Modified Lévy measure
ABSTRACT
The Student t-distribution can be applied in financial studies as heavy-tailed substitute to the normal distribution. The aim of this study is to explore the properties of Student t-distribution and Lévy -Student processes under finance. For a suitable modification of the Lévy measure of Student t-distribution, an explicit expression of its Fourier transform was calculated. It was shown that how the Fourier inversion of this function, which yields the density of the Lévy measure. Further, Lévy-student process is derived that nests the Brownian motion with subordinated by GIG distribution as parameters special case.
REFERENCES
[1] B. Mandelbrot, (1963), "The Variation of Certain Speculative Prices," The Journal of Business, 36, 394-419
[2] C. Halgreen, (1977), "Self-Decomposability of the Generalized Inverse Gaussian and Hyperbolic Distribution Functions," Z.Wahrschein. Verw.Gebiete, 47, 13-18.
[3] K. I. Sato, (1999), Lévy Processes and Infinitely Divisible Distributions, Cambridge: Cambridge University Press.
[4] B. Grigelionis, (2013), Student's T-Distribution and Related Stochastic Processes (Vol. 1), London: Springer.
[5] E. Grosswald, (1976), "The Student T-Distribution of Any Degree of Freedom Is Infinity Divisible," Z. Wahrscheinlichkeitstheor.verw.Geb, 36, 103-109.
[6] Z. J. Jurek, (2001), "Remarks on the Self-Decomposability and New Examples," Demonstration Mathematica XXXIV, 2, 241-250.
[7] C. Halgreen, (1989), "Self-Decomposability of the Generalized Inverse Gaussian and Hyperbolic Distributions," Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 47, 13-17 LA - English.
[8] S. Raible, (2000), " Lévy Processes in Finance: Theory, Numerics and Empirical Facts," PhD thesis, Freiburg University, Stockholm School of Economics.
[9] S. N. Kumari and and A. Tan, (2013), "Characterization of Student's T-Distribution with Some Application to Finance," Mathematical Theory and Modeling, 3, 1-9.
[10] N. Cufaro Petroni, S. De Martino, S. De Siena, and F. Illuminati, (2006), "Lévy-Student Processes for a Stochastic Model of Beam Halos," Nuclear Instruments and Methods in Physics Research A, 561, 237-243.
[11] G. Oliver and S. Rafael, (2010), "Scaling of Lévy Student Processes," Physica A, 389, 1455-1463.
[12] S. Nadarajah, and D. K. Dey, (2005), "Convolutions of the T-Distribution," Computers & Mathematics with Applications, 49.
[13] C. C. Heyde, and N. N. Leonenko, (2005), "Student Processes," Advances in Applied Probability, 37, 342-365.
[14] O. E Barndorff-Nielsen and N. Shephard, (2008), Financial Volatility: Stochastic Volatility and Lévy Based Models, Cambridge: Cambridge University Press.
|
