MTH512A - Foundations Of Mathematical Finance

Fundamentals of the financial markets, meaning of notions like asset portfolio derivatives (example: Futures, options forwards etc.)Binomial asset pricing model under no arbitrage condition single period model, multi period model. Risk neutral probabilities, martingales in the discrete frame work, risk neutral valuation of European and American options under no arbitrage condition in the binomial frame work. Introduction to continuous time models. Basic notions of probability theory on an infinite sample space. Change of measure and the Radon Nikodym derivative. Random walk and Brownian motion, Ito integral and Ito formula Black Scholes formula for pricing an European call option. Markowitz mean variance portfolio optimization problem. Single period and multi period model, Capital asset pricing model, outlines of the measures of risk, Value at Risk (VaR) and Conditional Value at Risk (CVaR).