Postgraduate Course: Discrete-Time Finance (MATH11153)
|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
|Summary||To introduce, in a discrete time setting, the basic probabilistic ideas and results needed for the conceptual understanding of the theory of stochastic process and its application to financial derivative pricing.
Introduction to background probability theory.
Discrete-time martingales, sub- and supermartingales.
Stopping Times, Optional Stopping Theorem, Snell Envelopes.
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.
Dividends in the binomial models.
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| None
Course Delivery Information
|Academic year 2021/22, Not available to visiting students (SS1)
|Learning and Teaching activities (Further Info)
Lecture Hours 18,
Seminar/Tutorial Hours 4,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
There will be 5 assignments (marked out of 10), each account for 1% of the course, and the students will get exactly what they get (without rounding up or down).
||The assignments will be marked and return to the students.
||Hours & Minutes
|Main Exam Diet S1 (December)||Discrete-Time Finance||2:00|
On completion of this course, the student will be able to:
- Demonstrate a conceptual understanding of conditional expectations.
- Demonstrate a thorough understanding of the Cox-Ross-Rubinstein binomial model and its application to option pricing problems.
- Demonstrate a conceptual understanding of the role of the risk-neutral pricing measure.
- Demonstrate a conceptual understanding of the role of equivalent martingale measures in financial mathematics.
- Demonstrate a conceptual understanding of the Optional Stopping problem, by answering relevant exam questions.
|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.
|Graduate Attributes and Skills
||MSc Financial Mathematics, MSc Financial Modelling and Optimization and MSc Computational Mathematical Finance students only.
|Course organiser||Dr Yvain Bruned
Tel: (0131 6)50 8572
|Course secretary||Miss Gemma Aitchison
Tel: (0131 6)50 9268