Artificial Intelligence for Option Pricing
Master’s thesis in Mathematical Sciences, specialisation in Finance Mathematics
Abstract
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.
Degree
Student essay
Collections
Date
2022-06-19Author
Hietanen, Emil
Keywords
Options, calls, puts, pricing, artificial neural networks, models, volatility, comparison
Language
eng