Machine learning in option pricing
1University of Oulu, Oulu Business School, Department of Finance, Finance
|Online Access:||PDF Full Text (PDF, )|
|Persistent link:|| http://urn.fi/URN:NBN:fi:oulu-201901091016
|Publish Date:|| 2019-01-09
|Thesis type:||Master's thesis
This paper gives an overview of the research that has been conducted regarding neural networks in option pricing. The paper also analyzes whether a deep neural network model has advantages over the Black-Scholes option pricing model in terms of pricing and hedging European-style call options on the S&P 500 stock index with data ranging from 1996 to 2014. While the previous literature has focused on shallow MLP-styled neural networks, this paper applies a deeper network structure of convolutional neural networks to the problem of pricing and hedging options. Convolutional neural networks are previously known for their success in image classification. The first chapters of this paper focus on both introducing neural networks for a reader, who is not familiar with the topic a priori, as well as giving an overview of the relevant previous literature regarding neural networks in option pricing. The latter chapters present the empirical methodology and the empirical results. The empirical study of this thesis focuses on comparing an option pricing model learned by a convolutional neural network to the Black-Scholes option pricing model. The comparison of the two pricing models is two-fold: the first part of the comparison focuses on pricing performance. Both models will be tested under a test set of data, computing error measures between the price predictions of each model against the true price of an option contract. The second part of the comparison focuses on hedging performance: both models will be used in a dynamic delta-hedging strategy to hedge an option position using the data that is available in the test set. The models are compared to each other using discounted mean absolute tracking error as a measure-of-fit. Bootstrapped confidence intervals are provided for all relevant performance measures. The empirical results are in line with the previous literature in terms of pricing performance and show that a convolutional neural network is superior to the Black-Scholes option pricing model in all error measures. The pricing results also show that a convolutional neural network is better than neural networks in previous studies with superior performance in pricing accuracy also when the data is partitioned by moneyness and maturity. The empirical results are not in line with the previous literature in terms of hedging results and show that a convolutional neural network is inferior to the Black-Scholes option pricing model in terms of discounted mean absolute tracking error. The main findings show that combining a neural network with a traditional parametric pricing formula gives the best possible outcome in terms of pricing and hedging options.
© Daniel Stafford, 2019. This publication is copyrighted. You may download, display and print it for your own personal use. Commercial use is prohibited.