Master's degree in Mathematics

Numerical methods for mathematical finance (seminar course)

Course code
4S001114
Name of lecturer
Leonard Peter Bos
Coordinator
Leonard Peter Bos
Number of ECTS credits allocated
6
Academic sector
MAT/08 - NUMERICAL ANALYSIS
Language of instruction
English
Period
II semestre dal Mar 2, 2020 al Jun 12, 2020.

Lesson timetable

Go to lesson schedule

Learning outcomes

The course will discuss various numerical methods for the pricing of the main financial instruments. An emphasis will be made on finance in the Energy industry. At the end of the course the student is expected to have the ability to construct and develop mathematical models for the stochastic processes of finance, to be able to analyze their limits and applicability and to solve them numerically.

Syllabus

Programme:

Binary Trees
Continuous time models (Geometric Brownian Motion, Black-Scholes, Feynman-Kac)
Estimating the volatility from historical data
Accelerating the back-folding of a tree
Path Dependent Options
Numerical Methods for Advection-Diffusion equations (Euler, Crank-Nicholson, application to the Black-Scholes PDE)
American and Asian Options
Jump Diffusions and the Merton Model
The Fast Gauss Transform and its application to the pricing of Options
Calibration of a model from historical data
Monte Carlo Methods
Numerical methods for SDE
Applications to Finance in Energy markets

Reference books
Author Title Publisher Year ISBN Note
L. Bos Course Notes 2017
P. Wilmott, S. Howison, J. Dewynne. The Mathematics of Financial Derivatives, A student introduction (Edizione 1) Cambridge University Press 1995

Assessment methods and criteria

To pass the exam the student must demonstrate the ability to mathematically model problems in finance and to solve them numerically using the methods discussed during the course. To that end the student will be assigned a project that will involve the implementation and study of some numerical methods for a problem in mathematical finance.





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