6 EC
Semester 1, period 1, 2
5374INRM6Y
| Owner | Master Mathematics |
| Coordinator | dr. A. Khedher |
| Part of | Master Stochastics and Financial Mathematics, Master Mathematics, Master Mathematics, specialization Stochastics , year 1 |
Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This course gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory.
The course is mainly theoretical.
|
Activity |
Number of hours |
|
Hoorcollege |
32 |
|
Oral exam |
1 |
|
Zelfstudie |
133 |
The programme does not have requirements concerning attendance (OER-B).
| Item and weight | Details |
|
Final grade |
There will be an oral exam for each part of the course. Erik Winands will give an oral exam for the first part of the course. Asma Khedher will give an oral exam for the second part of the course. To have the exam, you make an appointment with the lecturers.
The final grade is a combination of the results of the take home assignments (which counts 40 %) and the first and second oral exam (together 60%). To pass the course the average grade of both oral exams should be higher than 5.0.
The same applies in case of a resit. That is the final grade will be a combination of the results of the take home assignments (which counts 40 %) and the resit grade (60%).
Contact the course coordinator to make an appointment for inspection.
During the course, the students will have to hand in a total of six sets of homework. The average homework grade will count for 40% in the final grade.
The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl
| Weeknummer | Onderwerpen | Studiestof |
| 1 | Zero-coupon bonds, interest rates, coupon bonds, swaps | Chapter 2, Sections 2.1-2.4 |
| 2 | Yields, caps, floors, swaptions | Chapter 2, Sections 2.5-2.7 |
| 3 | Bootstrap, non-parametric estimation of term-structures | Chapter 3, Sections 3.1-3.2 |
| 4 |
No lecture Deadline of first take home assignment (all exercises of Section 2.8, except Exercise 2.7) |
|
| 5 | Principal component analysis | Chapter 3, Section 3.4 |
| 6 |
short rate models |
Chapter 5, Sections 5.1-5.4 |
| 7 | Standard models, default risk |
Chapter 5, Section 5.4 and Chapter 12, Sections 12.1-12.2 |
| 8 |
No lecture |
|
| 9 | Heath-Jarrow-Morton methodology | Sections 6.1-6.3 |
| 10 | Forward measures | Sections 7.1-7.3 |
| 11 | Affine processes | Sections 10.1 |
| 12 | Canonical state space | Section 10.2 |
| 13 | Discounting and pricing in affine models | Sections 10.3 |
| 14 | Market models | Section 11.1 - 11.2 |
| 15 | ||
| 16 |
The schedule for this course is published on DataNose.
Recommended prior knowledge: Measure theory, stochastic processes at the level of the course Measure Theoretic Probability, knowledge of stochastic integrals (key words: continuous time martingales, progressive processes, Girsanov transformation, stochastic differential equations) at the level of Stochastic Integration, knowledge of principles of financial mathematics, for instance at the level of Stochastic Processes for Finance.