First part: Monte Carlo Methods in Financial Engineering
1. Principles of Monte Carlo
Introduction; first examples; efficiency of simulation estimators.
2. Generating Random Numbers and Random Variables
Random number generation; general sampling methods; normal random variables and vectors.
3. Generating Sample Paths
Brownian motion; geometric Brownian motion; Gaussian short rate models; square-root diffusions; processes with jumps.
4. Variance Reduction Techniques
Control variates; antithetic variates.
5. Discretization Schemes
Euler scheme; convergence order; basics of second order schemes.
Second part: Exotic Options and Structured Products
6. Options Engineering: Organization and Applications
a) The Financial Engineering Organization
b) Options strategies, exotics
c) Financial Innovation risk management
7. Asian Options
Definition, pay-off, sensitivity and applications
8. Binary Options
Definition, pay-off, sensitivity and applications
9. Barrier Options
Definition, pay-off, sensitivity and applications
10. Structured Products
10.1. Structured Products on interest rates
10.2. Structured Products on exchange rates
10.3. Structured Products on Equity Assets
10.4. Structured Products on Credit
10.5. Certificates