Abstract
The geometric Brownian motion (Black–Scholes) model for the price of a risky asset stipulates that the log returns are i.i.d. Gaussian. However, typical log returns data shows a leptokurtic distribution (much higher peak and heavier tails than the Gaussian) as well as evidence of strong dependence. In this paper a subordinator model based on fractal activity time is proposed which simply explains these observed features in the data, and whose scaling properties check out well on various data sets.
AMS 1991 Subject Classification : Primary 90A09
Secondary 62M10; 60G18
Received 12 January 1998; revision received 28 January 1998.
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Heyde, C.C. (2010). A Risky Asset Model with Strong Dependence through Fractal Activity Time. In: Maller, R., Basawa, I., Hall, P., Seneta, E. (eds) Selected Works of C.C. Heyde. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5823-5_55
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