Ehrenfest Model with Large Jumps in Finance

TL;DR

This paper introduces an Ehrenfest model with large jumps to explain the empirical distribution of financial returns, which vary from stable distributions with heavy tails at short intervals to Gaussian at longer intervals.

Contribution

The paper proposes a novel Ehrenfest model with large jumps to unify the explanation of empirical financial data across different sampling intervals.

Findings

Empirical data shows stable distributions with alpha<2 at short intervals.

Long intervals exhibit Gaussian distribution of returns.

The ELJ model fits empirical density functions across intervals.

Abstract

Changes (returns) in stock index prices and exchange rates for currencies are argued, based on empirical data, to obey a stable distribution with characteristic exponent $ \alpha < 2 $ for short sampling intervals and a Gaussian distribution for long sampling intervals. In order to explain this phenomenon, an Ehrenfest model with large jumps (ELJ) is introduced to explain the empirical density function of price changes for both short and long sampling intervals.