Ehrenfest Model with Large Jumps in Finance

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.