Course co-ordinator(s): Dr Lukasz Szpruch (Edinburgh).
Aims:
Course for final year students in Honours programmes in Mathematics and/or Statistics.
Summary:
In this course we will cover the following topics:
- Random number generation, basic Monte Carlo, variance reduction techniques, simulating Brownian paths,
- Strong and weak approximations of solutions to SDEs,
- Euler’s approximations, Milstein’s scheme,
- Order of accuracy of the approximations,
- Higher order schemes, accelerated convergence
- Weak approximations of SDEs via numerical solutions of PDEs
- Option price sensitivities (Greeks).
Detailed Information
Pre-requisites: none.
Location: Edinburgh.
Learning Outcomes: Subject Mastery
On completion of the course the student should be able to:
- Understanding of Monte Carlo methods
- Ability to simulate random numbers from standard distributions
- Ability to numerically price some basic options
- Understanding of variance-reduction techniques
- Familiarity with numerical schemes for simulating solutions of SDEs.
- Ability to apply simple higher order schemes.
Reading list:
None
Assessment Methods:
Coursework 5%, Examination 95%, Main Exam 2 hrs
SCQF Level: 10.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the lecturer
VISION: further information and course materials are available on VISION