Journal of Applied Probability

A risky asset model with strong dependence through fractal activity time

C. C. Heyde

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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.

Article information

J. Appl. Probab. Volume 36, Number 4 (1999), 1234-1239.

First available in Project Euclid: 18 September 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 90A09
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60G18: Self-similar processes

Risky asset model Black-Scholes model heavy tails long-range dependence fractal activity time self-similarity


Heyde, C. C. A risky asset model with strong dependence through fractal activity time. J. Appl. Probab. 36 (1999), no. 4, 1234--1239. doi:10.1239/jap/1032374769.

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