A general fractional white noise theory and applications to finance

被引：180

作者：

Elliott, RJ

van der Hoek, J

机构：

[1] Univ Calgary, Haskayne Sch Business, Calgary, AB T2N 1N4, Canada

[2] Univ Adelaide, Dept Appl Math, Adelaide, SA, Australia

来源：

MATHEMATICAL FINANCE | 2003年 / 13卷 / 02期

关键词：

fractional Brownian motion; fractional white noise; Girsanov's theorem; Clark-Ocone representation theorem; fractional Black-Scholes market; fractional Ito isometry;

D O I：

10.1111/1467-9965.00018

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

摘要：

We present a new framework for fractional Brownian motion in which processes with all indices can be considered under the same probability measure. Our results extend recent contributions by Hu, Oksendal, Duncan, Pasik-Duncan, and others. As an application we develop option pricing in a fractional Black-Scholes market with a noise process driven by a sum of fractional Brownian motions with various Hurst indices.

引用

页码：301 / 330

页数：30

共 19 条

[1]

AASE K, 2000, FINANC STOCH, V4, P465

[2] Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns [J].