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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 I (MATH11076)

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 Credits7.5 ECTS Credits3.75
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 parameter martingales, sub- and super-martingales, martingale inequalities, optional sampling.
Wiener martingale, stochastic integral, the Itô calculus and some applications.
Multi-dimensional Wiener process, multi-dimensional Itô formula.
Stochastic differential equations
Change of measure, Girsanov's theorem, equivalent martingale measures and arbitrage.
Representation of martingales and the Ornstein-Uhlenbeck process.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Other requirements MSc Financial Mathematics and MSc Financial Modelling and Optimization students only.
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: 75 ( Lecture Hours 20, Summative Assessment Hours 1.5, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 51 )
Assessment (Further Info) Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
Additional Information (Assessment) See 'Breakdown of Assessment Methods' and 'Additional Notes', above.
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)Stochastic Analysis in Finance I (MATH11076) 3:00
Learning Outcomes
- be able to demonstrate an understanding of continuous time stochastic processes
- know the main results and basic applications of stochastic Ito calculus
- be able to understanding stochastic differential equations (SDE's)
- be able to understanding equivalent measures and in particular Girsanov's theorem
- conceptual understanding of martingales in continuous time.
- conceptual understanding of the stochastic Ito integral and It's formula.
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 and MSc Financial Modelling and Optimization students only.
Study Abroad Not Applicable.
KeywordsSAF I
Contacts
Course organiserProf Istvan Gyongy
Tel: (0131 6)50 5945
Email:
Course secretaryMr Brett Herriot
Tel: (0131 6)50 4885
Email:
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