Inference by Genetic Programming of an analytical expression for the Optimal Exercise Threshold of an asset that follows a Mean Reversion Process

The American option evaluation is a relatively complex and expensive process due to commonly used methodologies as Finite Differences, Dynamic Programming, Monte Carlo Simulation, etc. needs high computational performance. Besides that, the complexity needed to calculate the option value and the optimal threshold increases when the price of underlying asset follows the Mean Reversion Stochastic Process. By this way, is interesting to achieve an analytical approximation in order to make easier to obtain the optimal threshold and the option value. There are many analytical approximations mentioned in bibliography respecting to American Options about asset prices following a Geometric Brownian Motion [1] [2], but none about it follows Mean Reversion Processes. This work proposes a model based on Symbolic Regression by Genetic Programming to obtain an analytical approximation for the optimal threshold respecting to an American option which its asset follows a Mean Reversion Process. The Optimal Threshold that separates during the option life-cycle the decision to exercise the option, is later employed to evaluate the option. The result achieved by the proposed model (Threshold Analytical Function) seemed to be satisfactory.