A risky asset model with strong dependence through fractal activity time

C. C. Heyde

doi:10.1017/S0021900200018003

A risky asset model with strong dependence through fractal activity time

C. C. Heyde^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

57 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1234-1239
Number of pages	6
Journal	Journal of Applied Probability
Volume	36
Issue number	4
DOIs	https://doi.org/10.1017/S0021900200018003
Publication status	Published - Dec 1999

Access to Document

10.1017/S0021900200018003

Cite this

@article{c230bc6e296142e896364d14f8222336,

title = "A risky asset model with strong dependence through fractal activity time",

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.",

keywords = "Black-Scholes model, Fractal activity time, Heavy tails, Long-range dependence, Risky asset model, Self-similarity",

author = "Heyde, {C. C.}",

year = "1999",

month = dec,

doi = "10.1017/S0021900200018003",

language = "English",

volume = "36",

pages = "1234--1239",

journal = "Journal of Applied Probability",

issn = "0021-9002",

publisher = "Cambridge University Press",

number = "4",

}

TY - JOUR

T1 - A risky asset model with strong dependence through fractal activity time

AU - Heyde, C. C.

PY - 1999/12

Y1 - 1999/12

N2 - 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.

AB - 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.

KW - Black-Scholes model

KW - Fractal activity time

KW - Heavy tails

KW - Long-range dependence

KW - Risky asset model

KW - Self-similarity

UR - http://www.scopus.com/inward/record.url?scp=0033233850&partnerID=8YFLogxK

U2 - 10.1017/S0021900200018003

DO - 10.1017/S0021900200018003

M3 - Article

SN - 0021-9002

VL - 36

SP - 1234

EP - 1239

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 4

ER -

A risky asset model with strong dependence through fractal activity time

Abstract

Access to Document

Other files and links

Fingerprint

Cite this