# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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# 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 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.
 Pre-requisites Co-requisites Prohibited Combinations Students MUST NOT also be taking Simulation (MATH10015) Other requirements None
 Pre-requisites None High Demand Course? Yes
 Academic year 2015/16, Available to all students (SV1) Quota:  None Course Start Block 3 (Sem 2) Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 50 ( Lecture Hours 10, Supervised Practical/Workshop/Studio Hours 3, Programme Level Learning and Teaching Hours 1, Directed Learning and Independent Learning Hours 36 ) Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 % Additional Information (Assessment) Coursework 20% Examination 80% Feedback Not entered Exam Information Exam Diet Paper Name 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 Not entered Keywords MCM
 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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