## Topics

The course introduces students to advanced techniques for pricing derivative securities, using tools from continuous-time finance. The emphasis is on understanding unifying principles that can be applied to determine the price of simple as well as complex derivative securities. The associated techniques are the basic tools necessary to derive closed form formulas, such as the Black-Scholes-Merton model. Because prices of most contracts cannot be expressed in closed form a second focus of the course is the use of simulation techniques to implement the valuation principles. The obvious application of the techniques is to price financial contracts, like futures, options, swaps, etc. The same techniques can also be applied to estimate the present value of real assets essential in firms' investment decisions. The principles are then referred to as "real options theory", which is an important applied topic in the course. The principles for pricing derivative securities are based on basic insights that are crucial in risk management. By mastering techniques for pricing the securities, the students will thus also get access to tools necessary for determining useful 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
- Real options
- Simulations methods (discretization schemes, Monte Carlo)
- Aspects of financial risk management (Greeks, Value at Risk etc)