8392 - APPLIED NUMERICAL FINANCE

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 cannot be priced via closed formulae. We analyze derivatives on discontinuous underlying assets, focusing on the jump-diffusion model. Monte Carlo methods are then applied to price and to 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. Some sessions are devoted to the VBA (Visual Basic for Applications) implementation of algorithms presented in the classes.

• Pricing and hedging American and path-dependent options.
• Derivatives on several underlying assets. Currency markets.
• Jump-diffusion models.
• Monte Carlo methods in financial engineering: features, efficiency, and bias.
• Simulation of asset prices.
• Valuation of derivatives.
• Valuation of the greeks.
• Variance reduction techniques.
• Coding with VBA (Visual Basic for Applications).

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. The assignment has to be delivered the same day of the written exam and can be shared by a team of three 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.