Postgraduate Course: Simulation (MATH11083)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Not available to visiting students |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Credits | 15 |
| Home subject area | Mathematics |
Other subject area | Financial Mathematics |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | 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). |
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | MSc Financial Mathematics students only. |
| Additional Costs | None |
Course Delivery Information
|
| Delivery period: 2013/14 Semester 2, Not available to visiting students (SS1)
|
Learn enabled: Yes |
Quota: None |
Web Timetable |
Web Timetable |
| Course Start Date |
14/01/2014 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
150
(
Lecture Hours 20,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 3,
Directed Learning and Independent Learning Hours
125 )
|
| Additional Notes |
|
| Breakdown of Assessment Methods (Further Info) |
Written Exam
60 %,
Coursework
40 %,
Practical Exam
0 %
|
| Exam Information |
| Exam Diet |
Paper Name |
Hours:Minutes |
|
|
| Main Exam Diet S2 (April/May) | | 2:00 | | |
Summary of Intended Learning Outcomes
1. Ability to describe how to simulate random variables
of a given law.
2. understanding of the main variance-reduction methods
3. familiarity with simulating paths of Brownian motion
4. developing a critical awareness of the nature of random simulation and the types of errors associated with these approximations
5. Familiarity with numerical schemes for simulating solutions of SDEs.
6. Ability to apply simple higher order schemes. |
Assessment Information
| See 'Breakdown of Assessment Methods' and 'Additional Notes', above. |
Special Arrangements
| MSc Financial Mathematics students only. |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Random number generation, pseudorandom numbers, inversion method, acceptance/rejection method, Box-Muller method, basic Monte Carlo, quasi 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;
Option price sensitivities (Greeks). |
| Transferable skills |
Not entered |
| Reading list |
Law, A.M. & Kelton, D.W. (2000). Simulation Modelling and Analysis (3rd Edition). McGraw Hill.
Ripley, B.D. (1987). Stochastic Simulation. Wiley.
Dagpunar, J. S. (2007). Simulation and Monte Carlo: With applications in Finance and MCMC. Wiley. Associated software at http://www/wiley.com/go/dagpunar simulation.
Ross, S. M. (2002). Simulation (3rd ed.). Academic Press.
Boyle P, Broadie M, and Glasserman P (1997). Monte Carlo methods for security pricing, Journal of Economic Dynamics and Control, 4, 1267-1321. .
Hull, J. C. (2002). Options, Futures and Other Derivatives, 5th edition. Prentice Hall.
Glasserman, P. (2004). Monte Carlo methods in Financial Engineering. Springer.
Gentle, J.E. (2003). Random number generation and Monte Carlo methods, 2nd edition. Springer.
|
| Study Abroad |
Not Applicable. |
| Study Pattern |
See 'Breakdown of Learning and Teaching activities' above. |
| Keywords | SIM_FM |
Contacts
| Course organiser | Dr Lukasz Szpruch
Tel: (0131 6)50 5742
Email: L.Szpruch@ed.ac.uk |
Course secretary | Mrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk |
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