98722 - RISK MODELLING AND EVALUATION

Learning outcomes

At the end of the course the student is familiar with the main principles and tools of market risk analysis, pricing and the hedging techniques. He/she knows the general theory of risk measures and the principles of market risk regulation. He/she is able to design a process of market risk measurement and reporting, and to make market risk management decisions.

Course contents

This is a course on stochastic calculus for financial applications.

1. Construction of Brownian Motion and Wiener measure. Markovian, martingale and sample path properties of Brownian motion.
2. Continuous local martingales. Quadratic variation. Simple integrands and the elementary stochastic integral. Ito isometry.
3. Stochastic integration with respect to continuous local martingales. Ito's formula.
4. Equivalent changes of probability. Stochastic exponentials. Girsanov's theorem.
5. Brownian filtrations and the martingale representation theorem. Stochastic differential equations driven by Brownian motion.
6. Connections with partial differential equations. Cauchy problems and the Feynman-Kac representation.
7. Poisson and Levy processes. The Levy-Khinchine formula. Path decomposition of Levy processes. Stochastic integration with respect to jump-processes.

Readings/Bibliography

Steven E. Shreve, Stochastic Calculus for Finance II - Continuous-Time Models, ISBN: 978-0-387-40101-0

Teaching methods

The course includes weekly lectures and problem sessions. Some problem sessions may take place online.

Assessment methods

Assessment is based on a two-hour written final exam, consisting of a few problems in stochastic calculus and financial applications. The exam's valuation is based on the number of problem solved and on the completeness and accuracy of their solutions. The are no midterms.

Teaching tools

Textbook, lecture slides, problems.

Office hours

See the website of Paolo Guasoni

See the website of Sabrina Mulinacci