Postgraduate Course: Stochastic Analysis in Finance (MATH11154)
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 | 20 |
ECTS Credits | 10 |
| 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-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.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Course Delivery Information
|
| Academic year 2019/20, 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.
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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. |
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. |
| Keywords | SAF |
Contacts
| Course organiser | Prof Istvan Gyongy
Tel: (0131 6)50 5945
Email: |
Course secretary | Miss Gemma Aitchison
Tel: (0131 6)50 9268
Email: |
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