Prediction of Barrier Option Price Based on Antithetic Monte Carlo and Machine Learning Methods

Option pricing has become a popular topic in the fields of finance and mathematics with the rapid development of stock and option markets. Now, more and more academics, financial companies and investors are attracted to study and do research about it. The theory of option pricing can also be used to price financial instruments with the similar structure to options and contribute to risk control and management. The Black-Scholes model is the basic and famous method applied for different options pricing with modifications and adjustments, and the results can be solved by some traditional numerical methods such as the binomial model, finite difference method, Monte Carlo method and so on. Machine learning has risen recently and begins to replace some complex work in traditional methods with the evolution of computers and computing power. How to use machine learning methods to predict the option price is a problem worthy to be solved. In this research, using the antithetic Monte Carlo method generates the prices of the up-and-out barrier options without rebate based on the Black-Scholes model. The generated dataset is divided into a training set and a test set for support vector regression, random forest, adaptive boosting and artificial neural networks. We compare the fitting and performance of all machine learning methods and find that random forest and artificial neural network methods fit better than others with fewer errors in predictions.