English, Article edition: Stochastic integrals driven by fractional Brownian motion and arbitrage: a tale of two integrals Ngai Hang Chan; Chi Tim Ng

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Physical Description
  • article
Language
  • English

Edition details

Title
  • Stochastic integrals driven by fractional Brownian motion and arbitrage: a tale of two integrals
Author
  • Ngai Hang Chan
  • Chi Tim Ng
Physical Description
  • article
Notes
  • Recent research suggests that fractional Brownian motion can be used to model the long-range dependence structure of the stock market. Fractional Brownian motion is not a semi-martingale and arbitrage opportunities do exist, however. Hu and Øksendal [Infin. Dimens. Anal., Quant. Probab. Relat. Top., 2003, 6, 1-32] and Elliott and van der Hoek [Math. Finan., 2003, 13, 301-330] propose the use of the white noise calculus approach to circumvent this difficulty. Under such a setting, they argue that arbitrage does not exist in the fractional market. To unravel this discrepancy, we examine the definition of self-financing strategies used by these authors. By refining their definitions, a new notion of continuously rebalanced self-financing strategies, which is compatible with simple buy and hold strategies, is given. Under this definition, arbitrage opportunities do exist in fractional markets.
  • Fractional Brownian motion, Option pricing, Arbitrage pricing, Stochastic differential equations,
  • RePEc:taf:quantf:v:9:y:2009:i:5:p:519-525
Language
  • English
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