Some applications of log-ergodic processes: ergodic trading model and call option pricing using the irrational rotation

Due to the increasing popularity of futures trading among financial markets participants, the risk management of futures trading is of particular importance. In this paper, we study a futures trading strategy consisting of a long and a short positions by using the mean reversion property of positive log-ergodic financial processes. 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 an stochastic irrational rotation on the unit circle. By means of the properties of log-ergodic processes, we use the time average of the stochastic process of risky assets instead of expectation in our calculations. Our findings indicate that the proposed model improves the accuracy of predicting optimal trading times and enhances the computational efficiency of option pricing.