Registry
Module Specifications
Current Academic Year 2012 - 2013
Please note that this information is subject to change.
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| Description | |||||||||||||||||||||||||||||||||||||||||||||
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The module includes a practical introduction to the high level programming environment MATLAB. It also presents the theory of Monte Carlo simulation, and gives financial applications in the area of option pricing. The module includes substantial projects involving computer simulations in MATLAB.The module is aimed not only at masters students who have completed mathematical undergraduate programmes, but also students who have completed undergraduate courses in other disciplines including Engineering, Quantitative Finance and some fields of Science. A good knowledge of calculus, probability theory and linear algebra is required.Students are expected to attend lectures, tutorials and laboratories. They will also engage in group computer projects facilitated by a tutor, and individual projects. There is no formal end of module examination. | |||||||||||||||||||||||||||||||||||||||||||||
| Learning Outcomes | |||||||||||||||||||||||||||||||||||||||||||||
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1. Write clear, structured and well-organized programs in MATLAB and utilise the helpful resources which are available to users 2. Take into account accuracy and efficiency issues when designing and implementating MATLAB programs 3. Demonstrate a knowledge of elementary theory of Monte Carlo simulation 4. Use MATLAB to value various kinds of financial options using Monte Carlo simulation | |||||||||||||||||||||||||||||||||||||||||||||
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml |
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| Indicative Content and Learning Activities | |||||||||||||||||||||||||||||||||||||||||||||
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Review of Programming. Review elementary principles of programming. Introduction to MATLAB. Discussion of accuracy and efficiency issues in the implementation of numerical algorithms. Review of Probability. weak and strong laws of large numbers, stopping times, confidence intervals and central limit theorem. Simulating random variables. Generating uniform random numbers, inverse method for continuous and discrete random variables, acceptance-rejection method and application to normal and Gamma distribution; composition method and application to Gamma distribution. Monte Carlo methods in fiance. motivation for Monte Carlo methods in finance, controlling the error for Monte Carlo simulation, Monte Carlo integration; variance reduction by using antithetic variables. Option pricing with MATLAB. Models for continuous and discrete time asset price evolution, option prices as expectations, options and option prices in Black-Scholes model, Black-Scholes PDE and formulae, pricing Asian options using Monte Carlo methods, other exotic options. Implementing Monte Carlo simulation in MATLAB. Implementing Monte Carlo simulation in MATLAB. | |||||||||||||||||||||||||||||||||||||||||||||
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| Indicative Reading List | |||||||||||||||||||||||||||||||||||||||||||||
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| Other Resources | |||||||||||||||||||||||||||||||||||||||||||||
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| MFM | MSc in Financial Mathematics | ||||||||||||||||||||||||||||||||||||||||||||
| Timetable this semester: Timetable for MS450M | |||||||||||||||||||||||||||||||||||||||||||||
| Date of Last Revision | 21-JAN-10 | ||||||||||||||||||||||||||||||||||||||||||||
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