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:
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