Mathematical Finance

Overview

The course on ‘Mathematical Finance’ gives an introduction to this interesting and growing area. In particular, the course will cover two Nobel-prize winning frameworks, namely portfolio theory and the option pricing theory.

INTENDED AUDIENCE: Students at advanced undergraduate and postgraduate level in Mathematics, Statistics and allied areas as well as students of Engineering and Management interested in this field.PREREQUISITES: Background in basics of probability theoryINDUSTRY SUPPORT: Finance Industry

Syllabus

COURSE LAYOUT

Week 1: Introduction to financial markets, financial instruments, bonds, stocks and financial derivatives.Week 2: Time value of money, simple and compound interest rate, net present value, internal rate of return and annuities.Week 3: Markowitz portfolio theory, risk and return, two and multi asset portfolio theory, efficient frontier.Week 4: Capital Asset Pricing Model and portfolio performance analysis.Week 5: No arbitrage principle, pricing of forwards and futures, properties of options.Week 6: Derivative pricing by replication in binomial model.Week 7: Discrete probability spaces, filtration, conditional expectationWeek 8: Discrete time martingales, Markov chain, risk-neutral pricing in binomial model for European and American derivatives.Week 9: General probability spaces, conditional expectation, Brownian motion.Week 10: Ito integral, Ito formula, Girsanov’s theorem, martingale representation theorem, stochastic differential equation.Week 11: Black-Scholes-Merton (BSM) model, pricing of European derivatives in BSM framework.Week 12: Valuation of European options in BSM model, BSM formula, BSM partial differential equation, hedging, model completeness, fundamental theorems of asset pricing.