Postgraduate Course: Discrete-Time Finance (MATH11075)
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 | 15 |
ECTS Credits | 7.5 |
| Summary | 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. |
| Course description |
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
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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 2014/15, Not available to visiting students (SS1)
|
Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| 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 )
|
| 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 S1 (December) | MSc Financial Maths Discrete Time Finance | 2:00 | |
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.
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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.
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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 | 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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