Journal of Applied Probability

A risky asset model with strong dependence through fractal activity time

C. C. Heyde

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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.

Article information

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

Dates
First available in Project Euclid: 18 September 2002

Permanent link to this document
http://projecteuclid.org/euclid.jap/1032374769

Digital Object Identifier
doi:10.1239/jap/1032374769

Mathematical Reviews number (MathSciNet)
MR1746407

Zentralblatt MATH identifier
1102.62345

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

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

Citation

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. http://projecteuclid.org/euclid.jap/1032374769.


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