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A General Fractional White Noise Theory And Applications To Finance

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  • Robert J. Elliott
  • John Van Der Hoek

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.

Suggested Citation

  • Robert J. Elliott & John Van Der Hoek, 2003. "A General Fractional White Noise Theory And Applications To Finance," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 301-330, April.
    • Handle: RePEc:bla:mathfi:v:13:y:2003:i:2:p:301-330
    DOI: 10.1111/1467-9965.00018
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