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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: Stochastic Analysis in Finance (MATH11154)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) AvailabilityNot available to visiting students
SCQF Credits20 ECTS Credits10
SummaryThis course aims to provide a good and rigorous understanding of the mathematics used in derivative pricing and to enable students to understand where the assumptions in the models break down.
Course description Continuous time processes: basic ideas, filtration, conditional expectation, stopping times.
Continuous-time martingales, sub- and super-martingales, martingale inequalities, optional sampling.
Wiener process and Wiener martingale, stochastic integral, Itô calculus and some applications.
Multi-dimensional Wiener process, multi-dimensional Itô's formula.
Stochastic differential equations, Ornstein-Uhlenbeck processes, Black-Scholes SDE, Bessel processes and CIR equations.
Change of measure, Girsanov's theorem, equivalent martingale measures and arbitrage.
Representation of martingales.
The Black-Scholes model, self-financing strategies, pricing and hedging options, European and American options.
Option pricing and partial differential equations; Kolmogorov equations.
Further topics: dividends, reflection principle, exotic options, options involving more than one risky asset.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Other requirements None
Course Delivery Information
Academic year 2015/16, Not available to visiting students (SS1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 36, Seminar/Tutorial Hours 8, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 152 )
Assessment (Further Info) Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
Additional Information (Assessment) Examination 100%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)Stochastic Analysis in Finance (MATH11154)3:00
Learning Outcomes
It is intended that students will demonstrate
- understanding of continuous-time stochastic processes and their role in modelling the evolution of random phenomena,
- understanding of the Wiener process,
- conceptual understanding of the stochastic Itô integral and Itô's formula,
- conceptual understanding of the main results and basic applications of stochastic Ito calculus,
- understanding stochastic differential equations (SDE's),
- understanding of equivalent measures and in particular Girsanov's theorem.
- conceptual understanding of martingales in continuous time,
- understanding of the application of the theory of stochastic calculus to option pricing problems,
- understanding of the martingale representation theorem and its role in financial applications,
- conceptual understanding of the role of martingales in the theory of derivative pricing,
- conceptual understanding of the role of equivalent martingale measures in financial mathematics,
- conceptual understanding of SDEs in stochastic modelling and in particular in finance,
-understanding the concept of strategies in financial models,
by answering relevant exam questions.
Reading List
Karatzas, I. & Shreve, S. (1988). Brownian Motion and Stochastic Calculus. Springer.
Baxter, M. & Rennie, A. (1996). Financial Calculus. CUP.
Etheridge, A. (2002). A Course in Financial Calculus. CUP.
Lamberton, D. & Lapeyre, B. (1996). Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall.
Additional Information
Graduate Attributes and Skills Not entered
Special Arrangements MSc Financial Mathematics, MSc Financial Modelling and Optimization and MSc Computational Mathematical Finance students only.
KeywordsSAF
Contacts
Course organiserProf Istvan Gyongy
Tel: (0131 6)50 5945
Email:
Course secretaryMrs Kathryn Mcphail
Tel: (0131 6)51 4351
Email:
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