### 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.