Course Overview: This course covers some advanced numerical methods for a selection of important computational problems in finance, such as American options (obstacle problems), PDEs for multi-factor models (eg, from stochastic volatility), and the calibration of volatility models to quoted market prices. At the end of the course, the student should have a thorough understanding of the theory behind more advanced finite difference and calibration methods, be able to implement them for a range of applications, and have an appreciation of some of the current research areas.