Postgraduate Course: Simulation (MATH11083)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 15 |
ECTS Credits | 7.5 |
| Summary | 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). |
| Course description |
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).
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | MSc Financial Mathematics students only. |
Course Delivery Information
| Not being delivered |
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.
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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.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Special Arrangements |
MSc Financial Mathematics students only. |
| Study Abroad |
Not Applicable. |
| Keywords | SIM_FM |
Contacts
| Course organiser | Dr Lukasz Szpruch
Tel: (0131 6)50 5742
Email: L.Szpruch@ed.ac.uk |
Course secretary | Mr Thomas Robinson
Tel: (0131 6)50 4885
Email: Thomas.Robinson@ed.ac.uk |
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