Interest Rate Models

6 EC

Semester 1, period 1, 2

5374INRM6Y

Owner Master Mathematics
Coordinator dr. A. Khedher
Part of Master Mathematics, year 1Master Stochastics and Financial Mathematics, year 1

Course manual 2018/2019

Course content

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.

Study materials

Literature

  • Damir Filipovic, 'Term-Structure Model', Springer, ISBN 978-3-540-09726-6

Other

  • See also http://www.springer.com/mathematics/quantitative+finance/book/978-3-540-09726-6?changeHeader.

Objectives

  1. The student is able to recognize different contracts related to interest rates
  2. The student is able to communicate the statistics and estimation methods of the yield curve
  3. The student is able to explain why do we need yield curve models and to oversee the aspects and properties that an interest rate (curve) model should have
  4. The student is able to communicate standard short-rate models, to sketch the advantages and shortfalls from using these different short-rate models, and to differentiate their properties
  5. The student is able to apply the arbitrage theory to the HJM framework
  6. The student is able to explain why do we need the use of forward measures. Moreover, he is able to reproduce this theory to price options
  7. The student is able to explain affine models and to provide examples of such models. Moreover, The student is able to detect the advantages from the use of these models in the pricing formulas. The student is able to produce this theory in the context of stochastic volatility option pricing and the modeling of credit risk
  8. The student is able to develop an HJM-type model for the LIBOR rates and combine the theories studied to derive pricing formulas of the related contracts
  9. The student is able to recommend interest rate models that might fit well historical yield curves and reflect on the consequences of the choice of the model to the pricing of contracts

Teaching methods

  • Lecture
  • Self-study
  • Presentation/symposium

The course is mainly theoretical.

Learning activities

Activity

Number of hours

Hoorcollege

32

Oral exam

1

Zelfstudie

133

Attendance

The programme does not have requirements concerning attendance (OER-B).

Assessment

Item and weight Details

Final grade

60%

Oral exam

40%

Assignaments

There will be an oral exam for the course. Asma Khedher and Erik Winands will give the oral exam. 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 oral exam (60%). To pass the course the average grade of both oral exams should be higher than 5.0.

Inspection of assessed work

Contact the course coordinator to make an appointment for inspection.

Assignments

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.

Fraud and plagiarism

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

Course structure

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

Deadline of second take home assignment (Exercises 3.1, 3.3, 3.4, 5.2, 5.3, 5.6)

  
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 Implied bond market  Section 11.1 - 11.2
15    
16    

Timetable

The schedule for this course is published on DataNose.

Additional information

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.

Contact information

Coordinator

  • dr. A. Khedher

Staff

  • dr. ir. E.M.M. Winands