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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2013/2014 -
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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: Simulation (MATH11083)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityNot available to visiting students
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) Credits15
Home subject areaMathematics Other subject areaFinancial Mathematics
Course website None Taught in Gaelic?No
Course descriptionRandom 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.
KeywordsSIM_FM
Contacts
Course organiserDr Lukasz Szpruch
Tel: (0131 6)50 5742
Email: L.Szpruch@ed.ac.uk
Course secretaryMrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk
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