Mathematical Finance Seminar
February 27, 2003 , 5:30 PM to 7:00 PM
Martin Schaden, New York University
The Distributions of Historic Stock Returns and Quantum Theory
Abstract: The distributions of individual stock returns over time
periods
of
less than 2 weeks observed by ref.[1] are accurately modelled by the
square
of an amplitude that has the form of a Cauchy distribution. On time
scales
of
less than two weeks the only statistically relevant parameters of an
individual stock are the mean return and standard deviation of its
distribution of returns. I argue that the observed shape stability of
the
distribution for time periods from 5 minutes to 2 weeks rules out an
iid
process and is in general presents a problem for (most) stochastical
models.
I show that the distributions of the returns instead exhibit some
properties
one might expect from a quantum model. A very simple quantum
Hamiltonian
reproduces the observed short-term dynamics and, with a slight
modification,
semi-quantitatively gives the historic distribution of returns for
time
intervals up to 4 trading years.
[1] V Plerou, P.Gopikrishnan, L.N. Amaral, M. Meyer and H.E. Stanley,
Phys.Rev. E60, 6519 (1999).
The talk is an extended version of the preprint available from
this site .