Finance C / Foundations of Mathematical Finance

The lecture covers the following topics:

General background on derivative markets
Nature of derivatives, types of derivatives, applications of derivatives.

Fundamental mathematical concepts
Financial markets, arbitrage, linear products, arbitrage bounds.

Stochastic financial market models
Flow of information, trading strategies, wealth processes.

Risk neutral valuation
Arbitrage, martingale measures, risk neutral valuation, completeness.

Portfolio optimization
Risk preferences, utility functions, optimal portfolios.

Options and the stock market
Modelling stock prices, Black-Scholes-Merton model, mechanics of option markets.

Interest rates and futures
Time value of money, interest rates, bonds, term structure of interest rates, futures.

Swaps and FX products
Interest rate swaps, FX spot rates and outright forwards.

Credit risk and credit derivatives
Credit risk in swaps, credit risk in bonds, default probabilities, recovery rates, credit default swaps.

Risk measures
Introduction to risk management, value at risk, expected shortfall, historical simulation.