Postgraduate Course: Discrete-Time Finance (MATH11075)
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 | 15 |
| Home subject area | Mathematics |
Other subject area | Financial Mathematics |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | To introduce, in a discrete time setting, the basic probabilistic ideas and results needed for the later stochastic process and derivative pricing courses. By the end of the course students will be expected to understand discrete martingale theory and its relationship with financial concepts such as arbitrage. |
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: 2013/14 Semester 1, Not available to visiting students (SS1)
|
Learn enabled: Yes |
Quota: None |
Web Timetable |
Web Timetable |
| Course Start Date |
16/09/2013 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
150
(
Lecture Hours 34,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 3,
Directed Learning and Independent Learning Hours
111 )
|
| 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 S1 (December) | MSc Financial Maths Discrete Time Finance | 2:00 | | |
Summary of Intended Learning Outcomes
- identify and solve problems involving conditional expectation
- demonstrate a thorough understanding of the Cox-Ross-Rubinstein binomial model and apply it to option pricing problems
- demonstrate an understanding of the role of the risk-neutral pricing measure
- demonstrate an understanding of the main aspects of discrete-time martingale theory
- demonstrate an understanding of the Doob's Optional Stopping Theorem
- critical understanding of the Cox-Ross-Rubinstein model
- conceptual understanding of the role of the risk-neutral pricing measure
- conceptual understanding of the role of equivalent martingale measures in financial mathematics
- conceptual understanding of the Optional Stopping problem. |
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 |
I. Theory
Introduction to background probability theory.
Conditional expectation.
Discrete parameter martingales, sub- and supermartingales, martingale convergence and inequalities.
Stopping Times, Optional Stopping Theorem, Snell Envelopes
Stopping times and Doob's Optional Stopping Theorem
Central limit theorem (CLT)
Laws of large numbers (LLN)
II. Applications
Arbitrage and martingales, risk neutral measures.
Complete markets and discrete option pricing.
The binary tree model of Cox, Ross and Rubinstein for European and American option pricing (discrete Black-Scholes).
Dividends in the binomial models
Trinomial model (incomplete markets
Convergence of the CRR to the Black-Scholes model
|
| Transferable skills |
Not entered |
| Reading list |
Williams, D. (1991). Probability with Martingales. CUP.
Bingham, N.H. & Kiesel, R. (2004). Risk-Neutral Valuation. Pricing and Hedging of Financial Derivatives. Springer.
Baxter, M. & Rennie, A. (1996). 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 | DTF |
Contacts
| Course organiser | Dr Sotirios Sabanis
Tel: (0131 6)50 5084
Email: S.Sabanis@ed.ac.uk |
Course secretary | Mrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk |
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