2021/01/12 by Will Hicks, Hicks, Will
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications #q-fin.MF
paper · pdf · doi:10.48550/arxiv.2101.04604
openalex publication_date 2021/01/12 · arxiv created 2021/04/06 · arxiv updated 2021/04/07 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The application of the Cauchy distribution has often been discussed as a potential model of the financial markets. In particular the way in which single extreme, or "Black Swan", events can impact long term historical moments, is often cited. In this article we show how one can construct Martingale processes, which have marginal distributions that tend to the Cauchy distribution in the large volatility limit. This provides financial justification to approaches discussed by other authors, and highlights an example of how quantum probability can be used to construct non-Gaussian Martingales. We go on to illustrate links with hyperbolic diffusion, and discuss the insight this provides.