20247 - APPLIED NUMERICAL FINANCE
CLMG - M - IM - MM - AFC - CLEFIN-FINANCE - CLELI - ACME - DES-ESS - EMIT - GIO
Course taught in English
Go to class group/s: 31
The course provides the essential tools to understand and solve important computational issues in financial engineering. In particular, we deal with the valuation of American and exotic derivatives that do not admit closed form prices. We analyze derivatives on discontinuous underlying assets, focusing on the jump-diffusion model. Monte Carlo methods are then applied to price and hedge derivatives in diffusive models. We provide techniques to improve the efficiency and the accuracy of the Monte Carlo estimate of derivatives prices and sensitivities. Students are introduced to VBA (Visual Basic for Applications) and are tutored in the VBA implementation of the algorithms in the lab sessions. However VBA is not mandatory: Students proficient with MatLab (or other programming languages) are allowed to use MatLab instead of VBA for the assignment if they prefer so.
- Introduction to VBA (computer lab sessions).
- Pricing and hedging American and path-dependent options via lattice methods.
- Derivatives on several underlying assets. Currency markets.
- Jump-diffusion models.
- Monte Carlo methods in financial engineering: features, efficiency, and bias.
- Variance reduction techniques.
- Simulation of asset prices.
- Monte Carlo valuation of the greeks.
The brief written exam counts 70% and consists of open questions on the main arguments of the classes.
The assignment counts 30% and consists in writing a code to solve a selected problem as, for example, the evaluation of a particular path-dependent option, and a brief report on the related numerical/financial issues.
Students can choose to code with VBA or MatLab, or any other preferred language.
The list of assignment titles and instructions is provided during the course.
The assignment can be done in groups or individually, and is due the same day of the written exam. The assignment grade is valid until the end of the academic year.
The assessment is the same for attending and non attending students.
- Lecture Notes distributed by the instructor.
Intermediate quantitative skills (calculus, probability and algebra) are prerequisites for this course.