Date of Award

Summer 8-16-2024

Level of Access Assigned by Author

Open-Access Thesis

Degree Name

Master of Science (MS)

Advisor

Yifeng Zhu

Second Committee Member

Pankaj Agrrawal

Third Committee Member

Yonggang Lu

Abstract

This thesis aims to compare existing methodologies against new, transformer-based deep neural networks in predicting implied volatility (IV) of stock options. The implied volatility reflects investor sentiment regarding the underlying stock and provides insight into how the asset may move in price in the near future. Accurate prediction of IV can help investors allocate their holdings and improve option strategies to reduce risk in the process. As researchers test newer, more advanced models for predicting IV, the results improve when using traditional regression metrics such as root mean squared error (RMSE), but not when considering the Sharpe Ratio or how well the predicted information helps with trading. This research aims to compare existing methodologies against new, transformer-based deep neural networks in comparison to traditional and existing methods of predictions to determine whether these modified transformer-based models continue to improve the prediction of IV.

In this research, two Transformer models are examined: a vanilla Transformer and a Temporal Fusion Transformer (TFT). Both models were evaluated using a physics-informed loss function where the RMSE of predicted and actual IV was balanced with the RMSE of the Black-Scholes option pricing formula using predicted and actual IV as inputs. As a baseline, an LSTM model was fit to the data using the same Black-Scholes loss as the Transformers, along with a GARCH(1,1), which is one of the oldest methods for predicting IV.

Among the models evaluated, TFT significantly outperformed all others. However, the Transformer did not outperform the Long short-term memory (LSTM) models in all scenarios. Other combination/enhanced models were also tested – including a Bi-LSTM, an attn-LSTM, and an LSTM-Transformer – in response to the Transformer’s underperformance. In the end, the Transformer, LSTM-Transformer, and attn-LSTM underperformed the LSTM and Bi-LSTM when training utilized a physics-informed loss function.

The dataset used consists of a selection of S&P 500 stock options from February 2002 to December 2021 with daily values for Bid, Ask, Last, and the Greeks. To account for the difference of Black-Scholes option pricing formula between call and put options, the data was separated into calls and puts, choosing only the call options for which a corresponding put option existed since originally the plan was to run models for each set of data. However, due to the prohibitive size of the data and limitations on resources, only call options were used for training and validation.

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