Article2003

A General Fractional White Noise Theory And Applications To Finance

Robert James Elliott · John van der Hoek

301 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Fractional Differential Equations Solutions Fuzzy Systems and Optimization

Abstract

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, Øksendal, 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.

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References

1999Stochastic Analysis of the Fractional Brownian Motion 1951Multiple Wiener Integral 1997Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long‐Run in High Frequency Returns 1999A Practical Guide to Heavy Tails: Statistical Techniques and Applications 1997Arbitrage with Fractional Brownian Motion 2000Stochastic Calculus for Fractional Brownian Motion I. Theory 2003FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE

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2012A note on the use of fractional Brownian motion for financial modeling 2004An introduction to white–noise theory and Malliavin calculus for fractional Brownian motion 2003On arbitrage‐free pricing of weather derivatives based on fractional Brownian motion 2013MULTIFRACTIONAL STOCHASTIC VOLATILITY MODELS 2007Wavelet entropy of stochastic processes 2008The rate of convergence for Euler approximations of solutions of stochastic differential equations driven by fractional Brownian motion

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