After completing the course, students will be able to

• understand the no-arbitrage principle and its implications for asset pricing in complete and incomplete markets
• know the statistical properties of important continuous-time stochastic processes and are able to interpret and estimate the model parameters
• understand the concept of hedging in continuous time
• differentiate between the physical (empirical) and the equivalent risk-neutral (martingale) probability measure
• understand the general relation of asset prices to conditional expected payoffs under the risk-neutral measure
• understand and apply the Black-Scholes formula as an important example for an analytical model
• understand and apply the all-purpose concept of Monte-Carlo simulation to numerically compute expected pay-offs of arbitrary complexity under the risk-neutral measure

Although this course touches some very involved mathematical concepts (e.g., measure theory, stochastic calculus), the design of the course will only require prior knowledge in mathematics and statistics which could be expected from good students in economics and business administration showing some extra interest and motivation with respect to quantitative methods. In particular, students should be familiar with the concepts of partial derivatives, definite integrals, and conditional probabilities which could be refreshed by using any undergraduate textbook. As a consequence, students who might be interested in a rigorous treatment of the mathematical fundamentals are referred to graduate programs in this field or to suitable electives offered by the Institute for Statistics and Mathematics for undergraduate students.

One of the main course outcomes is the ability of students to compute fair values of financial instruments numerically with Monte-Carlo simulation. Although all cases and applications are designed in a way that MS Excel can still be used, a good command of R might be helpful.

The course will be delivered by in-class presentations in six units of 3:15 hours. Each unit will provide enough space for Q/A sessions. Two case studies have to be solved by students in take home assigments where feedback will be given individually.