Handbook

The course consists of two major parts. The first one is a more technical prerequisite of the second, but it delivers its own insights into the modelling of financial problems. It deals with Stochastic Calculus as a basis to model the stochastic development of asset prices, interest rates or latent variables. At the end of this part students should be familiar with Ito's Lemma and stochastic differential equations. This part asks for a positive attitude of students towards a more formal reasoning. It will take up about 30% of the lectures. 

The second part deals with a number of classical continuous-time applications in Finance. First, three problems which are based local on a no-arbitrage condition will be discussed: option pricing, structural models of credit risk, and the trade - off theory of the optimal capital structure. Second, portfolio theory and the characterization of expected asset returns in equilibrium will be analysed. These two problems were the first applications of the continuous-time finance approach. For the last topics, we have some flexibility: we can choose between several models that can be useful in a variety of settings, such as models with mean reversion, stochastic volatility, jumps, or regime switching. Alternatively, we could look at more sophisticated derivatives, such as term structure models, or models of credit default swaps.