TY - JOUR
T1 - Fractional Brownian motion as a weak limit of Poisson shot noise processes-with applications to finance
AU - Klüppelberg, Claudia
AU - Kühn, Christoph
N1 - Funding Information:
The authors thank Yuri Kabanov, Thomas Mikosch, and an anonymous referee for valuable comments on this paper. In addition, financial support by the Deutsche Forschungsgemeinschaft through the Graduiertenkolleg “Angewandte Algorithmische Mathematik” at Munich University of Technology is gratefully acknowledged by the second author.
PY - 2004/10
Y1 - 2004/10
N2 - 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.
AB - 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.
KW - Alternative stock price models
KW - Arbitrage
KW - Fractional Brownian motion
KW - Functional limit theorems
KW - Non-explosiveness of point processes
KW - Shot noise process
UR - http://www.scopus.com/inward/record.url?scp=4544374045&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2004.03.015
DO - 10.1016/j.spa.2004.03.015
M3 - Article
AN - SCOPUS:4544374045
SN - 0304-4149
VL - 113
SP - 333
EP - 351
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 2
ER -