Postgraduate Course: Monte Carlo Methods (MATH11155)
Course Outline
School | School of Mathematics |
College | College of Science and Engineering |
Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Available to all students |
SCQF Credits | 5 |
ECTS Credits | 2.5 |
Summary | This course aims to provide a good introduction to Monte Carlo methods with applications to finance. Topics that will be covered are: Random number generation, basic Monte Carlo, variance reduction techniques such as: importance sampling, control variates and antithetic random variable, Financial options price sensitivities (Greeks). Students are expected to implement above techniques in programming language such as Matlab. |
Course description |
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.
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Entry Requirements (not applicable to Visiting Students)
Pre-requisites |
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Co-requisites | |
Prohibited Combinations | Students MUST NOT also be taking
Simulation (MATH10015)
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Other requirements | None |
Information for Visiting Students
Pre-requisites | None |
High Demand Course? |
Yes |
Course Delivery Information
Not being delivered |
Learning Outcomes
On completion of this course, the student will be able to:
- Demonstrate conceptual understanding of Monte Carlo methods by answering relevant exam questions.
- Simulate pseudo random numbers from standard distributions by constructing relevant algorithms in reports and/or exams.
- Numerically price some basic financial options by constructing relevant algorithms in reports and/or exams.
- Demonstrate conceptual understanding of variance-reduction techniques and its importance for Monte Carlo simulations by answering relevant exam questions.
- Demonstrate conceptual understanding of various methods of calculating sensitivities for financial applications (Greeks) by answering relevant exam questions.
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Reading List
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.
Asmussen, S., Glynn, P. W., (2007) Stochastic Simulation: Algorithms and Analysis, Springer. |
Additional Information
Graduate Attributes and Skills |
Not entered |
Keywords | MCM |
Contacts
Course organiser | Dr Lukasz Szpruch
Tel: (0131 6)50 5742
Email: L.Szpruch@ed.ac.uk |
Course secretary | Miss Sarah McDonald
Tel: (0131 6)50 5043
Email: sarah.a.mcdonald@ed.ac.uk |
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