Using Logistic Regression of Machine Learning Method to Evaluate American Options

Aims: The main purpose of this study is to understand whether Logistic regression has certain benefits in the evaluation of American options. As far as the Monte Carlo method is concerned, the least square method is traditionally used to evaluate American options, but in fact, Logistic regression is generally quite good in classification performance. Therefore, this study wants to know if Logistic regression can improve the accuracy of evaluation in American options.

Study Design: The selection of options parameters required in the simulation process mainly considers the average level of actual market conditions in the past few years in terms of dividend yield and risk-free interest rate. The part of the stock price and the strike price mainly considers three different situations: in-the-money, out-of-the-money and at the money.

Methodology: This study applied the Logistic regression in Monte Carlo method for the pricing of American. Uses the ability of logistic regression to help determine whether the American option should be exercised early for each stock price path. The validity of the proposed method is supported by some vanilla put cases testing. The parameters used in all cases tested are considered the current state of the market.

Conclusion: This study demonstrates the effectiveness of the proposed approach using numerical examples, revealing significant improvements in numerical efficiency and accuracy. Several test cases showed that the relative error of all tests are below 1%.