Finance (2022/2023)

Learning outcomes

The course deals with the problem of how to evaluate financial derivative securities, showing how stochastic modeling of the dynamics of the underlying securities is operationally useful.
The basic principles of the risk neutrality approach are illustrated and practical results particularly used in quantitative finance are recalled.
It is then shown how the same concepts have been extended and analogous results have been obtained for more realistic models.

1. Preliminaries
Bonds, stocks
The problem of pricing derivatives
2. Equity prices
Pricing under uncertainty: stochastic models
Risk neutral pricing, risk aversion
3. Pricing derivatives
Risk hedging
Options prices and forward contracts
On the basis of the audience the following models will be treated: discrete single/multi-period models or models in continuous time and with continuous trajectories with constant or stochastic volatility or models in continuous time and with jumps.
4. The problem of selecting/estimating a model.

The exam consists of a series of presentations of assigned material to be studied and understood, and a written report containing the commented proof of a theoretical result.
For the exam to be passed it is necessary that the grade obtained is at least D.