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
|
---|---|
Authors: | Klüppelberg, Claudia ; Kühn, Christoph |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 113.2004, 2, p. 333-351
|
Publisher: |
Elsevier |
Keywords: | Shot noise process Alternative stock price models Functional limit theorems Fractional Brownian motion Arbitrage Non-explosiveness of point processes |
Saved in:
Saved in favorites
Similar items by person
-
On the existence and uniqueness of Glosten-Milgrom price processes
Riedel, Matthias, (2013)
-
Game contingent claims in complete and incomplete markets
Kühn, Christoph, (2004)
-
How local in time is the no-arbitrage property under capital gains taxes?
Kühn, Christoph, (2019)
- More ...