A Quantum Approach to Stock Price Fluctuations
| dc.creator | Schaden, Martin | |
| dc.date | 2002-05-20 | |
| dc.date | 2003-05-09 | |
| dc.date.accessioned | 2026-07-07T12:07:28Z | |
| dc.date.available | 2026-07-07T12:07:28Z | |
| dc.description | A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals this amplitude is proportional to a Cauchy-distribution and satisfies the Schroedinger equation with a non-hermitian Hamiltonian. The observed power law tails of the return fluctuations imply that the "decay rate", $γ(q)$ asymptotically is proportional to $|q|$, for large $|q|$. The wave number, the Fourier-conjugate variable to the return, is interpreted as a quantitative measure of "market sentiment". On a time scale of less than a few weeks, the distribution of returns in this quantum model is shape stable and scales. The model quantitatively reproduces the observed cumulative distribution for the short-term normalized returns over 7 orders of magnitude without adjustable parameters. The return fluctuations over large time periods ultimately become Gaussian if $γ(q\sim 0)\propto q^2$. The ansatz $γ(q)=b_T\sqrt{m^2+q^2}$ is found to describe the positive part of the observed historic probability of normalized returns for time periods between T=5 min and $T\sim 4$ years over more than 4 orders of magnitude in terms of one adjustable parameter $s_T=m b_T\propto T$. The Sharpe ratio of a stock in this model has a finite limit as the investment horizon $T\to 0$. Implications for short-term investments are discussed. | |
| dc.description | 24 pages, 4 figures, revised and extended version of "The Stock Price Distribution in Quantum Finance" | |
| dc.identifier | https://arxiv.org/abs/physics/0205053 | |
| dc.identifier | http://arxiv.org/abs/physics/0205053 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208981 | |
| dc.subject | Physics and Society | |
| dc.subject | Data Analysis, Statistics and Probability | |
| dc.subject | Statistical Finance | |
| dc.title | A Quantum Approach to Stock Price Fluctuations | |
| dc.type | text |