Research On Option Pricing Algorithm Based On Gaussian Process Regression And Monte Carlo Simulatio

Over the past 40 years,derivatives have become increasingly important in finance,trading activity has become more frequent,and the pricing of financial derivatives is one of the most important issues in financial markets.Options,as very important financial derivatives,have developed to an increasingly large type and transaction size,increasingly complex trading strategies,increasing data differences,and more featurerich options require a large amount of historical data for backtesting.The classical pricing method based on Monte Carlo simulation is characterized by large computational volume,time-consuming computation,and strong model and parameter dependence,resulting in the computation of option prices are not real-time,posing a huge challenge to complex option pricing and risk management.With the trend of expanding computational resources and dataset size,machine learning has developed into a core area of computational engineering,and the application of machine learning techniques in finance has brought new development opportunities for derivatives pricing.Therefore,in this thesis,we propose a new approach of machine learning techniques combined with Monte Carlo simulation for option price prediction.For several common path-dependent option pricing problems,we achieve several orders of magnitude acceleration by deploying Gaussian Process Regression(GPR)-based machine learning techniques,and the main work of this thesis is as follows:To avoid the situation that the Black-Scholes pricing formula has too many assumptions and the volatility is a constant that does not match the data observed in the actual market,we choose the Heston stochastic volatility model,which is representative in the field of financial derivatives pricing.Using this model to price derivatives,under the risk-neutral harnessing theory,the Heston stochastic volatility model can accurately portray the variation of financial asset prices in the actual market and obtain the corresponding three option pricing formulas,based on which the general process of option price path simulation can be obtained in combination with the Monte Carlo method,thus generating the basic data applicable to the option price prediction model.The option pricing model is trained by Gaussian process regression method(GPR),and the final option price prediction model is obtained by selecting the appropriate parameters and optimizing them under the action of RBF kernel function.Next,the option prices predicted by three nonparametric machine learning models(support vector regression SVR,Gaussian process regression GPR,and kernel ridge regression KRR)are compared and analyzed to compare the prediction performance of different methods for option pricing.Finally,the option prices obtained from Monte Carlo simulations are used as baseline to analyze the predictive ability of the three regression pricing models.To address the time-consuming training of GPR models,we use the GPy Torch framework built on Py Torch with GPU acceleration to solve the problem of timeconsuming training of GPR models due to the large amount of computation and reduce the time required for model training and prediction.An optimization scheme for combining kernel functions is proposed,which effectively utilizes the GPU and achieves fast pricing of several path-dependent options.