9th Symposium on Finance, Banking, and Insurance
Universität Karlsruhe (TH), Germany, December 11 - 13, 2002

Abstract


 


 


Subordinated Stock Price Models:
Heavy Tails and Long-Range Dependence in the High-frequency Deutsche Bank Price Record

  
 

Carlo Marinelli1 and Hermann Göppl2

   
 

1 Department of Electronics and Computer Science
University of Padova, Italy
2 Institute of Decision Theory and Marketing Research
University of Karlsruhe, Germany



 
 

Following a previous study on subordinated exchange rate models, we investigate the main properties of the high-frequency Deutsche Bank price record in the setting of stochastic subordination and stable modeling, focusing on heavy-tailedness and long memory, together with their dependence on the sampling period. We find that the market time process has increments described well by Gamma distributions, and that the log price process in intrinsic time can be approximated, at different time scales, by &alpha-stable Lévy processes. Most importantly, long-range dependence with strong intensity is present in the market time process, with an estimated Hurst index H approx. 0.9. Finally, the stable domain of attraction offers a good fit of the returns in physical time, which display weak long memory. As a consequence, we propose as a realistic model for the stock prices a process Z(t) subordinated to an a­stable Lévy motion S(t) by a long-memory intrinsic time process T (t) with Gamma-distributed increments.