Some Applications of Log-Ergodic Processes: Ergodic Trading Model and Call Option Pricing Using the Irrational Rotation

TL;DR

This paper introduces a novel ergodic trading model for optimal exit timing and applies ergodic theorems to European call option pricing using irrational rotations, emphasizing time averages over expectations.

Contribution

It presents new applications of log-ergodic processes in financial modeling, specifically for trading strategies and option pricing with irrational rotations.

Findings

Effective estimation of optimal trading exit times.

Application of ergodic theorems to option pricing.

Use of time averages for risk asset modeling.

Abstract

Due to the increasing popularity of futures trading among financial market participants, the risk management of these instruments is crucial. In this paper, we introduce a model for estimating the ideal time for leaving a trading position on a stock. Also, using ergodic theorems, we investigate the European call option pricing problem using a stochastic irrational rotation on the unit circle. Utilizing the properties of log-ergodic processes, we use the time average of the stochastic process of risky assets instead of expectations in our calculations.