Postgraduate Course: Stochastic Analysis in Finance I (MATH11076)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 7.5 |
ECTS Credits | 3.75 |
| Summary | 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. |
| 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.
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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
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| 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.
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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.
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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. |
| Keywords | SAF I |
Contacts
| Course organiser | Prof Istvan Gyongy
Tel: (0131 6)50 5945
Email: |
Course secretary | Mr Brett Herriot
Tel: (0131 6)50 4885
Email: |
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