Volatility modelling and calibration by optimal transport

This thesis studied volatility models for option pricing and their calibration methods using the optimal transport theory. The author first introduced theoretical results by casting a class of volatility model calibration problems as a type of convex optimisation problem. Based on the established results, the author proposed calibration methods with numerical methods to calibrate the local volatility model, stochastic volatility model and a joint model for SPX and VIX. The proposed methods efficiently and accurately capture the market dynamics.