Non-Linear Option Pricing

Prerequisites: familiarity with Brownian motion, Itô's formula, stochastic differential equations, and Black-Scholes option pricing. Prerequisites: Familiarity with Brownian motion, Itô's formula, stochastic differential equations, and Black-Scholes option pricing. Nonlinear Option Pricing is a major and popular theme of research today in quantitative finance, covering a wide variety of topics such as American option pricing, uncertain volatility, uncertain mortality, different rates for borrowing and lending, calibration of models to market smiles, credit valuation adjustment (CVA), transaction costs, illiquid markets, super-replication under delta and gamma constraints, etc. The objective of this course is twofold: (1) introduce some nonlinear aspects of quantitative finance, and (2) present and compare various numerical methods for solving high-dimensional nonlinear problems arising in option pricing.