Model for Non-Gaussian Intraday Stock Returns

TL;DR

This paper introduces a model explaining the non-Gaussian, stable distribution of intraday stock returns by assuming constant intraday volatility that varies over longer periods, fitting data from the London Stock Exchange.

Contribution

The paper presents a novel model linking long-term volatility variation to intraday return distributions, validated with extensive empirical data.

Findings

Returns are non-Gaussian and stable over intraday scales.

The model accurately fits empirical return distributions.

Returns follow a Student distribution due to gamma-distributed volatility.

Abstract

Stock prices are known to exhibit non-Gaussian dynamics, and there is much interest in understanding the origin of this behavior. Here, we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations (called intraday returns) and verify the model using a large database for several stocks traded on the London Stock Exchange. We provide evidence that the return distribution for these stocks is non-Gaussian and similar in shape, and that the distribution appears stable over intraday time scales. We explain these results by assuming the volatility of returns is constant intraday, but varies over longer periods such that its inverse square follows a gamma distribution. This produces returns that are Student distributed for intraday time scales. The predicted results show excellent agreement with the data for all stocks in our study and over all regions of the return distribution.