Learning outcomes

Numerical methods for derivative pricing and risk managment:
- tree methods;
- finite differences methods (implicit, explicit, Crank-Nicholson)
- Monte Carlo methods.
Each of the above topic includes practical implementations with Matlab.
TEXTBOOKS:
P. Wilmott, "Paul Wilmott introduces quantitative finance", Wiley 2006
P. Glasserman, "Monte Carlo methods for financial engineering", Springer 2004

Program

Scope of the course is the introduction of the main numerical methods used for numerical computation of financial quantities, derivative pricing and risk evaluation in finance. Such methods will be developed with the use of the software Matlab.
In particular, the following topics will be treated:
- Tree methods for the pricing of European contingent claims and empirical check of the convergence of the results to the Black and Scholes formula in the case of put and call options. Computation of the delta. Application of the methods in the case of American contingent claims.
- Finite differences methods (implicit, explicit, Crank-Nicholson) for the pricing of European and American contingent claims. Stability and convergence.
- Monte Carlo methods: Euler scheme for the simulation of trajectories of stochastic processes: the case of the Black and Scholes model and of the stochastic volatility models. Use of Monte Carlo methods for derivative pricing and for the computation of Value at Risk.

TESTI:
P. Wilmott, "Paul Wilmott introduces quantitative finance", Wiley 2006
P. Glasserman, "Monte Carlo methods for financial engineering", Springer 2004

Examination Methods

The exam is developed in two parts: a practical work with Matlab, followed by a spoken exam. The practical work is organized in exercises and will last 3 hours. The spoken exam is devoted to the assessment of student's learning during the course, the understanding of items, the ability to connect knowledges.