Aims:
The course deals with a rigorous introduction to Monte Carlo methods, and numerical methods to find solutions to stochastic differential equations. These methods are immensely important to understanding financial options price sensitivities (Greeks), and so applications to the techniques discussed will be to finance. Students will be expected to understand both the theoretical content, but also to be able to implement numerical techniques in a programming language such as Matlab.
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Linked course(s): F71SF Stochastic Analysis In Finance (Linked).
Location: Edinburgh.
Semester: 2.
Syllabus:
Topics covered in the course include: Random number generation, pseudorandom numbers, inversion method, acceptance/rejection method, Box-Muller method, basic Monte Carlo, quasi Monte Carlo.
Variance reduction techniques such as: importance sampling, control variates and antithetic random variable, Option price sensitivities (Greeks): pathwise,
likelihood and finite difference approaches.
Burkholder-Davis-Gundy inequality and Gronwall' s lemma. Strong and weak approximations of solutions to SDEs. Euler's approximations and Milstein's scheme. Order of accuracy of numerical approximations. Higher order schemes, accelerated convergence. Weak approximations of SDEs via numerical solutions of PDEs.
Learning Outcomes: Subject Mastery
On completion of this course, the student will be able to:
1. Be able to simulate random numbers from standard distributions.
2. Be able to use Monte-Carlo techniques to analyse stochastic differential equations.
3. Be able to numerically price basic financial options.
4. Be able to use various numerical schemes to simulate solutions to stochastic differential equations.
5. Be able to use variance-reduction techniques, and to be able to explain their importance.
Assessment Methods: Due to covid, assessment methods for Academic Year 2020-21 may vary from those noted on the official course descriptor. Please see the Computer Science Course Weightings and the Maths Course Weightings for 2020-21 Semester 1 assessment methods.
SCQF Level: 11.
Credits: 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