Artificial Intelligence for Option Pricing
Master’s thesis in Mathematical Sciences, specialisation in Finance Mathematics
This thesis addresses the issue of vulnerable underlying assumptions used in option pricing methodology. More precisely; underlying assumptions made on the financial assets and markets make option pricing theory vulnerable to changes in the financial framework. To enhance the robustness of option pricing, an alternative approach using artificial intelligence is introduced. Artificial intelligence is an advantageous tool for pricing financial assets and instruments, in particular; the use of deep neural networks as one does not have to make any assumptions. Instead, the neural network learns the underlying patterns of the asset and market directly from the input data. To test the proposed pricing alternative, an error metrical analysis, a log-returns distribution fit, and a volatility-smile fit is performed. Four mathematical option pricing models are used as reference models; Black–Scholes, Merton jump-diffusion model, Heston stochastic volatility model and Bates stochastic volatility with jumps. In addition, three types of neural networks are used; multilayer perceptron (MLP), long short-term memory (LSTM), and convolutional neural network (CNN). All methods included in the thesis require some predefined set of parameters, therefore, a parameter calibration method is required. A non-linear least square method can be used for cases where the number of combinations is sufficiently small. However, as the possible number of parameter combinations increases, the method becomes too computationally heavy. To combat this, an evolutionary reinforcement machine learning algorithm is introduced to find a set of calibrated parameters in a more efficient approach. First versions of option pricing neural networks show great promise, with significantly better results than the reference models. In addition, the networks show good coherence to existing stylized facts of options, in terms of the empirical frequency distribution of log-returns and volatility smile fit.