High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following properties: (i) They are not Gaussian and their center is well adjusted by Levy distributions. (ii) They are long-tailed but have finite moments of any order. (iii) They are self-similar on many time scales. Finally, (iv) at small time scales, price volatility follows a non-diffusive behavior. We extend Merton's ideas on speculative price formation and present a dynamical model resulting in a characteristic function that explains in a natural way all of the above features. The knowledge of such distribution opens a new and useful way of quantifying financial risk. The results of the model agree -with high degree of accuracy- with empirical data taken from historical records of the Standard & Poor's 500 cash index.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Length: Date of creation: Mar 2000 Date of revision: Publication status: Published in Physica A 283 (2000) 559-567 Handle: RePEc:arx:papers:cond-mat/0003357
For technical questions regarding this item, or to correct its listing, contact: (arXiv administrators).
Related research
Keywords:
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)