Learning outcomes

The course introduces the basic principles of financial economics and the basic computational and quantitative methods required to manage and evaluate financial securities in the presence of risk and uncertainty. The first part is devoted to the discussion of the principle of absence of arbitrage opportunities and to the risk neutral valuation approach. The first and second fundamental theorem of asset pricing are discussed and their use is practically exemplified in the analysis of financial markets and of firms' capital structure decisions. In the second part of the course the focus is on decision theory and on the representation of agents' preferences using the expected utility maximization procedure in a static and dynamic framework. In the dynamic framework the Bellman Optimality Principle is introduced and applied to the valuation of financial securities and to the analysis of intertemporal investment and consumption choices.

Program

Arbitrage and financial valuation.

Linear factor models. The CAPM (Capital Asset Pricing Model) as a factor model. Market efficiency and theory of valuation based on the absence of arbitrage opportunities. Relationship between market equilibrium and arbitrage. Ross formulation of APT (Arbitrage Pricing Theory). Statistics and data. Empirical tests of the CAPM and the APT. Roll's critique. Fama and French model.

The absence of arbitrage opportunities and risk neutral valuation. The one period model with a finite number of states of nature. State prices. First and Second Fundamental Theorems of Finance. An application to financial markets: simplified model of contingent claims valuation. An application to the modern theory of capital structure: Modigliani-Miller's Theorems. The relationship between the Modigliani-Miller model and the CAPM.

Financial decision making under uncertainty.

Single-period models. Utility functions. Von Neumann Morgenstern Preference Representation Theorem. Expected utility and paradoxes. Absolute and relative risk aversion . Expected utility maximization criterion for the optimal investment choice.

Multi-period models. Basic stochastic calculus. Conditional expectation in a discrete framework. Stopping times. Markov processes. Bellman's optimality principle. An application to financial valuation: options with american exercise type. An application to the consumption-investment choice: CCAPM (Consumption Capital Asset Pricing Model). Financial implications of the CCAPM optimality conditions.

Examination Methods

Students obtain the final grade by giving a compulsory written test and an optional oral exam.