The emphasis of the course is on understanding general principles that can be applied to price simple as well as complex derivatives. We use the economic principles and tools to derive closed form formulas, such as the Black-Scholes-Merton model. Because prices of most derivatives cannot be expressed in closed form an important focus of the course is the use of Monte Carlo simulation techniques to estimate derivative prices numerically. While the obvious application of the techniques is to price financial contracts, like futures, options, swaps, etc., the same techniques can be applied to estimate the present value of real assets; an important input in firms' investment decisions. When applied to real assets the principles are referred to as "real options methods", which is an important applied topic in the course. The principles for pricing derivative assets are based on basic insights that are crucial in risk management. By mastering techniques for pricing derivatives, students will thus also work with tools that are important for determining appropriate financial risk management strategies.

Topics:

Repetition of the binomial model

- Modeling asset prices in continuous time as diffusions
- The Black Scholes model I: the traditional approach (PDEs)
- The Black Scholes model II: the "modern" approach (risk-adjusted probabilities)
- Modeling commodities spot and futures prices
- Fixed income securities
- Real options
- Simulations methods (discretization schemes, Monte Carlo)
- Aspects of financial risk management (Greeks, Value at Risk etc)