Postgraduate Course: Stochastic Analysis in Finance I (MATH11076)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Not available to visiting students |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Credits | 7.5 |
| Home subject area | Mathematics |
Other subject area | Financial Mathematics |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | This 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. |
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. |
| Additional Costs | None |
Course Delivery Information
|
| Delivery period: 2014/15 Semester 1, Not available to visiting students (SS1)
|
Learn enabled: Yes |
Quota: None |
|
Web Timetable |
Web Timetable |
| Course Start Date |
15/09/2014 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
75
(
Lecture Hours 24,
Summative Assessment Hours 1.5,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
48 )
|
| Additional Notes |
|
| Breakdown of Assessment Methods (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
|
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | | 3:00 | |
Summary of Intended 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. |
Assessment Information
| See 'Breakdown of Assessment Methods' and 'Additional Notes', above. |
Special Arrangements
| MSc Financial Mathematics and MSc Financial Modelling and Optimization students only. |
Additional Information
| Academic description |
Not entered |
| Syllabus |
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.
|
| Transferable skills |
Not entered |
| 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.
|
| Study Abroad |
Not Applicable. |
| Study Pattern |
Not entered |
| Keywords | SAF I |
Contacts
| Course organiser | Prof Istvan Gyongy
Tel: (0131 6)50 5945
Email: |
Course secretary | Dr Jenna Mann
Tel: (0131 6)50 4885
Email: |
|
© Copyright 2014 The University of Edinburgh - 13 February 2014 1:48 pm
|
University Homepage