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Modelling of Bonds, Term Structure & Interest Rate Derivatives (Online Version) - MAT00019M

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  • Department: Mathematics
  • Module co-ordinator: Prof. Tomasz Zastawniak
  • Credit value: 20 credits
  • Credit level: M
  • Academic year of delivery: 2021-22

Related modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Module will run

Occurrence Teaching cycle
A1 Autumn Term 2021-22 to Spring Term 2021-22
A2 Autumn Term 2021-22 to Summer Term 2021-22
B1 Spring Term 2021-22 to Summer Term 2021-22
B2 Spring Term 2021-22

Module aims

The module introduces the probabilistic concepts and techniques necessary for modelling the dynamics of interest rates. The mathematical theory of interest rates is complex, since on the one hand it has to cover simultaneous random behaviour of a family of bonds indexed by maturity, and on the other hand be consistent with no-arbitrage restrictions. Additionally, to be realistic models have to be complex enough to enable the calibration of their parameters to real data. The complexity stems from the fact that in general interest rates depend on running time and maturity time, so are stochastic processes of two time variables, each with a very specific role. Discrete models will be constructed based on tree structures. For some special models a continuous time limit results in a stochastic differential equation of Ito type. In full generality the theory of partial stochastic differential equations is needed to investigate sophisticated models (this issue is only briefly outlined in the module). However, there is no such thing as the best or universally accepted model. Hence this module shows a variety of approaches and much time is devoted to the study of their relationships. One crucial issue is concerned with fitting the model to the data, called calibration. Pricing interest rate derivative securities is of great importance, since they represent a vast majority of the derivatives traded.

Module learning outcomes

By the end of this module students should

  • be able to construct arbitrage-free models of interest rates and the term structure of bond prices in the binary tree model and to price interest rate derivatives within such a model;
  • be able to price complex interest rate derivative securities, including American and exotic options, in a discrete setting with random interest rates of various maturities;
  • be able to price various derivative securities (such as caps, floors, swaps) written on bonds as underlying securities;
  • understand the features of various models describing the dynamics of interest rates and be able to see the connections between them, in both the discrete and continuous time frameworks;
  • demonstrate skills necessary for practical implementation of the techniques, in particular, be able to calibrate selected models

Assessment

Task Length % of module mark
Essay/coursework
Assignment
N/A 100
Oral presentation/seminar/exam
Online Viva
N/A 0

Special assessment rules

None

Reassessment

Task Length % of module mark
Essay/coursework
Assignment
N/A 100
Oral presentation/seminar/exam
Online Viva
N/A 0

Module feedback

Information currently unavailable

Indicative reading

1. M. Capinski and T. Zastawniak, Mathematics for Finance, Chapters 10, 11. Springer-Verlag, London 2003.
2. R. Jarrow, Modelling Fixed Income Securities and Interest Rate Options, McGraw-Hill, New York 1996.
3. T. Bjork, Arbitrage Theory in Continuous Time, Oxford University Press, Oxford 1998.



The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.