Postgraduate Course: Monte Carlo Methods (MATH11155)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Available to all students
|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.
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.
Entry Requirements (not applicable to Visiting Students)
|Prohibited Combinations|| Students MUST NOT also be taking
||Other requirements|| None
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2017/18, Available to all students (SV1)
||Block 3 (Sem 2)
|Learning and Teaching activities (Further Info)
Lecture Hours 10,
Supervised Practical/Workshop/Studio Hours 3,
Programme Level Learning and Teaching Hours 1,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Hours & Minutes
|Main Exam Diet S2 (April/May)||Monte Carlo Methods (MATH11155) ||1:00|
| 1. Demonstrate conceptual understanding of Monte Carlo methods by answering relevant exam questions.
2. Demonstrate the ability to simulate pseudo random numbers from standard distributions by constructing relevant algorithms in reports and/or exams.
3. Demonstrate the ability to numerically price some basic financial options by constructing relevant algorithms in reports and/or exams.
4. Demonstrate conceptual understanding of variance-reduction techniques and its importance for Monte Carlo simulations by answering relevant exam questions.
5. Demonstrate conceptual understanding of various methods of calculating sensitivities for financial applications (Greeks) by answering relevant exam questions.
|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.
|Graduate Attributes and Skills
|Course organiser||Dr Lukasz Szpruch
Tel: (0131 6)50 5742
|Course secretary||Ms Hannah Burley
Tel: (0131 6)50 4885