Lecturers are: Professor Patrick Gagliardini (University of Lugano & the Swiss Finance Institute) and Professor Eric Renault (Brown University) The lectures will be organized around eight themes in the following order: 1. The role of stochastic volatility in option pricing. Options prices as expectations of a Black-Scholes price. The volatility smile. 2. Non-linear State-Space models. 3. Extensions of the Generalized Method of Moments (GMM) to accommodate latent variables: Indirect Inference and Implied-States GMM. 4. Nonparametric methods to fit the implied volatility surface. Implied binomial trees and maximum entropy. 5. High-frequency data and option pricing. 6. The Extended Method of Moments (XMM). 7. Volatility risk premium and long memory in volatility. 8. VIX computation and methods for American options.