Bayesian kernel machine for derivatives pricing and forecasting

Abstract

According to advances in information technology, many machine learning techniques have been developed to take advantages of the vast amounts of data, which overcome the limitations of conventional parametric models. Especially in financial engineering, the stochastic volatility or jumps models have supported 'volatility-smile' of the actual data against unrealistic assumptions of Black-Scholes model. However the parametric methods still have some limits on determining option pricing accurately, so the research based on the non-parametric methods has been developed to increase the performance of prediction. Although neural network models, which are the representative forecasting methods, give the point-estimates to input values, the models do not provide any confidence level of the values. The distribution of option prices includes more useful and reliable information for prediction, when traders manage the risk of the portfolio. Gaussian processes regression is one of the supervised learning methods, which give the distribution of non-linear function by training the covariance of labeled data. Since the method finds the optimal parameters of kernel functions by assuming a specific form of covariance function, it enables us to avoid over-fitting and find the optimal hyper-parameters by the principled way. Therefore, Gaussian processes regression has been a notable tool in data mining and financial engineering. Firstly, we propose a transductive Bayesian regression method by learning non-linear manifold to reduce features of high-dimensional data. This method presents the underlying structure using prior information, and then provides the distribution of predicted values. Since a direct application of Bayesian regression to the option pricing takes a long time and gives the unreliable outputs, we need to find out the essential factors of high-dimensional data. Simulation results exhibit the effective and consistent performance of the proposed method using benchmark data and real-world data. Next, based on the proposed dimension reduction method, we develop a positive Bayesian regression method using a new transform measure, which can reasonably reject the properties of call option price. The proposed method provides not only the non-negative distribution of option prices, but also the probabilistic distribution of large deviations. The experimental results verify the statistically significant performance of the proposed method compared to other non-parametric methods using KOSPI 200 Index option data. Lastly, we compare the performance of parametric and non-parametric methods, focusing on Gaussian processes regression, for prediction of KOSPI 200 Index option prices. Using 10 years of data, the performance of state-of-art non-parametric methods is validated both in-sample pricing and out-of-sample prediction. Experimental results exhibit that the non-parametric methods outperform the stochastic volatility or jump models as well as the Black-Scholes model. Gaussian processes regression shows the most superior performance, especially in periodical predictions. In conclusion, the proposed methods are mainly based on the Gaussian process regression methods and focused on forecasting the distribution of KOSPI 200 Index option prices. We aim to provide a new Bayesian kernel method which enhances the predictive distribution of option prices with non-linear manifold. These Bayesian regression methods can be utilized in a wide range of business intelligence such as text mining, social network analysis, and marketing. We expect that the proposed methods will pave the way for Bayesian kernel machines to be applied to the various decision support systems and hedging of more complex derivatives.