20247 - APPLIED NUMERICAL FINANCE
CLMG - M - IM - MM - AFC - CLAPI - CLEFIN-FINANCE - CLELI - ACME - DES-ESS - EMIT
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 will be introduced to VBA (Visual Basic for Applications) and will be tutored in the VBA implementation of the algorithms in the lab sessions. VBA is a flexible programming language, whose knowledge is considerably appreciated among employers because VBA’s vast array of applications (also in non financial corporations). However VBA is not mandatory: Students proficient with MatLab (and who prefer it) are allowed to use MatLab instead of VBA for the assignment. All algorithms and numerical recipes dealt with in class will be available both in VBA and in MatLab on the web-page of the course.
Introduction to VBA (computer lab sessions).
Pricing and hedging American and path-dependent options via lattice methods.
Derivatives on several underlying assets. Currency markets.
Monte Carlo methods in financial engineering: features, efficiency, and bias. Variance reduction techniques.
Simulation of asset prices.
Monte Carlo Valuation of derivatives and their greeks.
The assessment is constituted by an assignment and a brief written exam. The brief written exam consists in answering questions concerning the main arguments of the classes. The assignment consists in writing a code to solve a selected problem (e.g. the evaluation of a particular path-dependent option), and a brief report on the related numerical/financial issues. You may choose to code with VBA or MatLab, if you prefer.
The assignment has to be delivered the same day of the written exam and can be shared by a team of five students at the most (but can also be done individually).
The assessment is the same for attending and non attending students.
- P. GLASSERMAN, Monte Carlo Methods in Financial Engineering, Springer, 2003 (Selected topics from chapters 1, 2, 3, 4 and 7).
- A. BATTAUZ, Topics in Quantitative Finance, Lecture Notes distributed by the instructor.
Intermediate quantitative skills (calculus, probability and algebra) are prerequisites for this course.