Title: Innovative derivative pricing and time series simulation techniques via machine and deep learning
Description: There is a growing number of applications of machine learning and deep learning in quantitative and computational finance. In this thesis, we focus on two of them. In the first application, we employ machine learning and deep learning in derivative pricing. The models considering jumps or stochastic volatility are more complicated than the Black-Merton-Scholes model and the derivatives under these models are harder to be priced. The traditional pricing methods are computationally intensive, so machine learning and deep learning are employed for fast pricing. I n Chapter 2, we propose a method for pricing American options under the variance gamma model. We develop a new fast and accurate approximation method inspired by the quadratic approximation to get rid of the time steps required in finite difference and simulation methods, while reducing the error by making use of a machine learning technique on pre-calculated quantities. We compare the performance of our method with those of the existing methods and show that this method is efficient and accurate for practical use.

In Chapters 3 and 4, we propose unsupervised deep learning methods for option pricing under Lévy process and stochastic volatility respectively, with a special focus on barrier options in Chapter 4. The unsupervised deep learning approach employs a neural network as the candidate option surface and trains the neural network to satisfy certain equations. By matching the equation and the boundary conditions, the neural network would yield an accurate solution. Special structures called singular terms are added to the neural networks to deal with the non-smooth and discontinuous payoff at the strike and barrier levels so that the neural networks can replicate the asymptotic behaviors of options at short maturities. Unlike supervised learning, this approach does not require any labels. Once trained, the neural network solution yields fast and accurate option values. The second application focuses on financial time series simulation utilizing deep learning techniques. Simulation extends the limited real data for training and evaluation of trading strategies.

It is challenging because of the complex statistical properties of the real financial data. In Chapter 5, we introduce two generative adversarial networks, which utilize the convolutional networks with attention and the transformers, for financial time series simulation. The networks learn the statistical properties in a data-driven manner and the attention mechanism helps to replicate the long-range dependencies. The proposed models are tested on the S&P 500 index and its option data, examined by scores based on the stylized facts and are compared with the pure convolutional network, i.e. QuantGAN. The attention-based networks not only reproduce the stylized facts, including heavy tails, autocorrelation and cross-correlation, but also smooth the autocorrelation of returns.