| dc.description.abstract | Options hedging is a critical problem in financial risk management. The prevailing approach in financial derivative pricing and hedging has been to first assume a parametric model describing the underlying price dynamics. An option model function is then calibrated to current market option prices and various sensitivities are computed and used to hedge the option risk. It has been recognized that computing hedging position from the sensitivity of the calibrated model option value function is inadequate in minimizing the variance of the option hedging risk, as it fails to capture the model parameter dependence on the underlying price.
We propose several data-driven approaches to directly learn a hedging function from the historical market option and underlying data by minimizing certain measures of the local hedging risk and total hedging risk. This thesis will focus on answering the following questions: 1) Can we efficiently build direct data-driven models for discrete hedging problems that outperform existing state-of-art parametric hedging models based on the market prices? 2) Can we incorporate feature selection and feature extraction into the data-driven models to further improve the performance of the discrete hedging? 3) Can we build efficient models for both the one-step local risk hedging problem and multi-step total risk hedging problem based on the state-of-art learning framework such as deep learning framework and kernel learning framework?
Using the S&P 500 index daily options data for more than a decade ending in August 2015, we first propose a direct data-driven approach based on kernel learning framework and we demonstrate that the proposed method outperforms the parametric minimum variance hedging method, as well as minimum variance hedging corrective techniques based on stochastic volatility or local volatility models. Furthermore, we show that the proposed approach achieves significant gain over the implied Black-Sholes delta hedging for weekly and monthly hedging.
Following the direct data-driven kernel learning approach, we propose a robust encoder-decoder Gated Recurrent Unit (GRU) model, for optimal discrete option hedging. The proposed model utilizes the Black-Scholes model as a pre-trained model and incorporates sequential information and feature selection. Using the S&P 500 index European option market data from January 2, 2004, to August 31, 2015, we demonstrate that the weekly and monthly hedging performance of the proposed model significantly surpasses that of the data-driven minimum variance (MV) method, the regularized kernel data-driven model, and the SABR-Bartlett method.
In addition, the daily hedging performance of the proposed model also surpasses that of MV methods based on parametric models, the kernel method, and the SABR-Bartlett method.
Lastly, we design multi-step data-driven models to hedge the option discretely until the expiry. We utilize the SABR model and Local Volatility Function (LVF) to augment existing market data and thus alleviate the problem of scarcity in market option prices. The augmented market data is used to train a sufficient total risk hedging model. | en |
