Fractional Brownian motion as a weak limit of Poisson shot noise processes--with applications to finance

Claudia Klüppelberg and Christoph Kühn

Stochastic Processes and their Applications, 2004, vol. 113, issue 2, 333-351

Abstract: We consider Poisson shot noise processes that are appropriate to model stock prices and provide an economic reason for long-range dependence in asset returns. Under a regular variation condition we show that our model converges weakly to a fractional Brownian motion. Whereas fractional Brownian motion allows for arbitrage, the shot noise process itself can be chosen arbitrage-free. Using the marked point process skeleton of the shot noise process we construct a corresponding equivalent martingale measure explicitly.

Keywords: Shot; noise; process; Alternative; stock; price; models; Functional; limit; theorems; Fractional; Brownian; motion; Arbitrage; Non-explosiveness; of; point; processes (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (7)

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