The Student subordinator model with dependence for risky asset returns. (English) Zbl 1277.62212
Summary: A new, tractable model of the stock price due to C.C. Heyde [J. Appl. Probab. 36, No. 4, 1234–1239 (1999; Zbl 1102.62345)] (see also [C.C. Heyde and N.N. Leonenko, Adv. Appl. Probab. 37, No. 2, 342–365 (2005; Zbl 1081.60035)]) is elaborated here and used for asset price movement. The model is driven by a Brownian motion, which has a “fractal clock” rather than a calendar clock. We incorporate the Student’s \(t\)-distribution, and a special dependence structure is introduced through the construction of this fractal time. The Student model described has desired features supported by real financial data.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 60F05 | Central limit and other weak theorems |
| 60G10 | Stationary stochastic processes |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 60G15 | Gaussian processes |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60J65 | Brownian motion |
| 91B25 | Asset pricing models (MSC2010) |
References:
| [1] | DOI: 10.1214/aop/1176988503 · Zbl 0839.60024 · doi:10.1214/aop/1176988503 |
| [2] | DOI: 10.1080/713665670 · doi:10.1080/713665670 |
| [3] | DOI: 10.1016/S0167-7152(02)00032-9 · Zbl 1001.60020 · doi:10.1016/S0167-7152(02)00032-9 |
| [4] | DOI: 10.1239/jap/1152413733 · Zbl 1103.62103 · doi:10.1239/jap/1152413733 |
| [5] | DOI: 10.1142/S0219024908005093 · Zbl 1175.91178 · doi:10.1142/S0219024908005093 |
| [6] | DOI: 10.1016/j.jeconom.2004.09.002 · Zbl 1334.62004 · doi:10.1016/j.jeconom.2004.09.002 |
| [7] | DOI: 10.1239/jap/1032374769 · Zbl 1102.62345 · doi:10.1239/jap/1032374769 |
| [8] | Heyde , C. C. , Gay , R. ( 2002 ). Fractals and contingent claims. Austral. National University Preprint . |
| [9] | DOI: 10.1239/aap/1118858629 · Zbl 1081.60035 · doi:10.1239/aap/1118858629 |
| [10] | Heyde C. C., J. Korean Math. Soc. 38 pp 1047– (2001) |
| [11] | DOI: 10.1007/978-94-011-4607-4 · doi:10.1007/978-94-011-4607-4 |
| [12] | Rosenblatt , M. ( 1961 ). Independence and dependence.Proc. 4th Berkeley Symp. Math. Stat. Prob.Berkeley, CA: University of California Press, pp. 441–443 . |
| [13] | DOI: 10.1111/j.1751-5823.2000.tb00329.x · Zbl 1107.91365 · doi:10.1111/j.1751-5823.2000.tb00329.x |
| [14] | DOI: 10.1007/BF00532868 · Zbl 0303.60033 · doi:10.1007/BF00532868 |
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