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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: 2020-21

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## Module will run

Occurrence Teaching cycle
A1 Autumn Term 2020-21 to Spring Term 2020-21
A2 Autumn Term 2020-21 to Summer Term 2020-21
B1 Spring Term 2020-21 to Summer Term 2020-21
B2 Spring Term 2020-21 to 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

None

### Reassessment

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

## Module feedback

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