Bubbles and crashes in a Black–Scholes model with delay

John Appleby (), Markus Riedle () and Catherine Swords ()

Finance and Stochastics, 2013, vol. 17, issue 1, 30 pages

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

Keywords: Stochastic functional differential equation; Resolvent; Renewal equation; Brownian motion; Law of the iterated logarithm; Efficient market hypothesis; 91B26; 91B70; 34K50; 34K25; G14 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00780-012-0181-4

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