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 expectation
Week 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.