# The Wandering of Corn

## TL;DR

This paper analyzes the discrete and stochastic nature of corn futures trading, challenging continuous price theories and proposing new probabilistic models for trading volume, price increments, and extreme events.

## Contribution

It introduces novel distributions and relationships for modeling corn futures trading data, emphasizing the discrete, non-Gaussian, and non-equilibrium aspects of price movements.

## Key findings

- Waiting times fit Kumaraswamy distribution better than Weibull.
- Empirical frequencies of extreme increments resemble forked tongues in plots.
- Dependence between increments suggests a stochastic process for variances.

## Abstract

Time and Sales of corn futures traded electronically on the CME Group Globex are studied. Theories of continuous prices turn upside down reality of intra-day trading. Prices and their increments are discrete and obey lattice probability distributions. A function for systematic evolution of futures trading volume is proposed. Dependence between sample skewness and kurtosis of waiting times does not support hypothesis of Weibull distribution. Kumaraswamy distribution is more suitable for waiting times. Relationships between trading volume and maximum profit strategies are presented. Frequencies of absolute b-increments are approximated by a Hurwitz Zeta distribution. Relative b-increments are non-Gaussian too. Dependence between b- and a-increments allows to interpret the sample variances of b-increments as a stochastic process. Mean sample variance of b-increments vs. a-increments is presented. The L1 distance and Log-likelihood statistics for independence between a- and b-increments are controversial. Corn price jumps remind of chain branching reactions. Bi-logarithmic plots of the empirical frequencies of extreme b-increments vs. ranks are presented. Corresponding distributions resemble snakes forked tongues. The maximum profit strategy is discussed as a measure of non-equilibrium.