Artificial intelligence algorithms in quantitative finance

Summary Artificial intelligence has become increasingly popular in quantitative finance with the increase in computational capabilities as well as model complexity and has led to many financial applications. In this thesis, we explore three different applications to solve challenges in the financial derivatives domain ranging from model selection, to model calibration, to derivative valuation. In Part I, we focus on a volatility regime-switching model to value equity derivatives. The model parameters are estimated using the Expectation-Maximization (EM) algorithm and a local volatility component is added so that the model is calibrated to vanilla option prices using the particle method. In Part II, we then use deep neural networks to calibrate a stochastic volatility model, in which volatility is represented by the exponential of an Ornstein-Uhlenbeck process, to approximate the function that relates the model parameters to the corresponding implied volatilities offline. Once the costly approximation is done offline, the calibration reduces to a standard and fast optimization problem. In Part III, we finally use deep neural networks to value American options on large baskets of stocks to overcome the curse of dimension. Different methods are studied with a Longstaff-Schwartz approach, where we approximate the continuation values, and a stochastic control approach, where we solve the partial differential valuation equation by reformulating it into a stochastic control problem using the nonlinear Feynman-Kac formula.