Financial Mathematics II
Discrete-time financial models and riskless asset pricing. Notion of arbitrage, martingale measure, and complete and incomplete markets. Fundamental theorems of asset pricing. Static and dynamic hedging and replication. Change of numeraire and equivalent martingale measures. Introduction to options and risk-neutral pricing. Stopping times and American option pricing. Introduction to the Black-Scholes theory and sensitivity analysis for options. Optional topics: introduction to single-factor interest rate modelling and pricing of fixed income securities.