A wave function for stock market returns

Ataullah, Ali; Davidson, Ian and Tippett, Mark (2009). A wave function for stock market returns. Physica A: Statistical Mechanics and its Applications, 388(4) pp. 455–461.

DOI: https://doi.org/10.1016/j.physa.2008.10.035

Abstract

The instantaneous return on the Financial Times-Stock Exchange (FTSE) All Share Index is viewed as a frictionless particle moving in a one-dimensional square well but where there is a non-trivial probability of the particle tunneling into the well’s retaining walls. Our analysis demonstrates how the complementarity principle from quantum mechanics applies to stock market prices and of how the wave function presented by it leads to a probability density which exhibits strong compatibility with returns earned on the FTSE All Share Index. In particular, our analysis shows that the probability density for stock market returns is highly leptokurtic with slight (though not significant) negative skewness. Moreover, the moments of the probability density determined under the complementarity principle employed here are all convergent — in contrast to many of the probability density functions on which the received theory of finance is based.