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Bubbles and crashes in a Black–Scholes model with delay

Author

Listed:
  • John Appleby
  • Markus Riedle
  • Catherine Swords

Abstract

This paper studies the asymptotic behaviour of an affine stochastic functional differential equation modelling the evolution of the cumulative return of a risky security. In the model, the traders of the security determine their investment strategy by comparing short- and long-run moving averages of the security’s returns. We show that the cumulative returns either obey the law of the iterated logarithm, but have dependent increments, or exhibit asymptotic behaviour that can be interpreted as a runaway bubble or crash. Copyright Springer-Verlag 2013

Suggested Citation

  • John Appleby & Markus Riedle & Catherine Swords, 2013. "Bubbles and crashes in a Black–Scholes model with delay," Finance and Stochastics, Springer, vol. 17(1), pages 1-30, January.
    • Handle: RePEc:spr:finsto:v:17:y:2013:i:1:p:1-30
    DOI: 10.1007/s00780-012-0181-4
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    References listed on IDEAS

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    4. Jean-Philippe Bouchaud & Rama Cont, 1998. "A Langevin approach to stock market fluctuations and crashes," Science & Finance (CFM) working paper archive 500027, Science & Finance, Capital Fund Management.
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    More about this item

    Keywords

    Stochastic functional differential equation; Resolvent; Renewal equation; Brownian motion; Law of the iterated logarithm; Efficient market hypothesis; 91B26; 91B70; 34K50; 34K25; G14;
    All these keywords.

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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