Handbook

The theory of Option Pricing represents one of the success stories of modern Finance. Not only is the theory elegant and tractable mathematically, it has had enormous practical relevance to the development of complex financial instruments whose prices are contingent on underlying traded and non-traded assets. It paved the way for the analysis of finance problems from very different fields in continuous time. The most prominent areas are portfolio management, asset pricing, and the management of market and credit risk, optimal capital structure, and general equilibrium theory.

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 Itoâ??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 one third of the lectures.

The second part deals with a number of classical continuous-time applications in Finance. First, three problems which areas 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 continuousâ??time finance approach. The last topics are devoted to no-arbitrage term structure theories and to the general equilibrium theory as developed by Cox/Ingersoll/Ross.