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.

Constructing applicable automated stock trading strategies has become one of the best ways that people can earn profits from their underlying assets' investments now. Automated stock trading, also called quantitative trading, contains sets of human-defined rules, which are written in codes to make decisions to go long or short on stocks on a computer. Investment banks, brokerages, private equity funds, and other financial institutions around the world are keen on investigating and developing quantitative trading strategies with sustainable profitability to yield higher returns than the normal market. This research aims to observe the trading performance and profits of financial banking stocks in the Hong Kong stock market by building a quantitative trading strategy named Enhanced Bollinger Band Strategy based on Random Forest and Bollinger Bands. In experiments, the Random Forest algorithm is applied to predict the Weighted Moving Average the next day. Meanwhile, Bollinger Bands are the trading signals used to make decisions on going long or short positions based on the historical moving average lines and standard deviation. Performances of the Enhanced Bollinger Band Strategy are evaluated by test sets of ten financial banking stocks. We also compare the performance of the Enhanced Bollinger Band Strategy and Traditional Bollinger Band Strategy and find that the Enhanced Bollinger Band Strategy can earn 10-30% profits on a variety of stocks although these stocks are losing 10-50% original amount of investment in Traditional Bollinger Band Strategy and basic investment. Therefore, a combination of Random Forest and Bollinger Bands in the quantitative trading strategy generates higher returns than simply investing in stocks.