Fractional Brownian motion as a weak limit of Poisson shot noise processes--with applications to finance
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.
Year of publication: |
2004
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Authors: | Klüppelberg, Claudia ; Kühn, Christoph |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 113.2004, 2, p. 333-351
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Publisher: |
Elsevier |
Keywords: | Shot noise process Alternative stock price models Functional limit theorems Fractional Brownian motion Arbitrage Non-explosiveness of point processes |
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