Profit and Loss Distributions on a Market of Single Futures Contract

Abstract

Profit and loss distributions of trading strategies with position limits and transactions costs are divided on industry gain and traders interest and determined for a single futures contract. Open interest and volume are expressed for a multiset of strategies with constraints. These strategies are more complicated than Dyck and Motzkin paths. A generating polynomial for the number of integer partitions with labeled parts in a multiset and two algorithms are presented. Weibull, Gamma, Kumaraswamy distributions for sample statistics of skewness and excess kurtosis of tick volumes are discussed.