### Module Details

 The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
 Title INTEREST RATE THEORY Code MATH481 Coordinator Professor OO Menoukeu Pamen Mathematical Sciences O.Menoukeu-Pamen@liverpool.ac.uk Year CATS Level Semester CATS Value Session 2023-24 Level 7 FHEQ Second Semester 15

### Aims

1. To provide a general foundation for pricing and hedging of financial derivatives, and an analysis of various market models.

2. To introduce the typical stochastic interest rate models, and pricing and hedging methodologies of financial derivatives in such a setting.

3. To give a detailed analysis of basic fixed-income securities, such as bonds, swaps, caps, swapations, caplets, and floorlets.

### Learning Outcomes

(LO1) At the end of the module students should have: 1.    A critical awareness of current problems and research issues in the field of financial derivatives, interest rate models, and fixed-income securities. 2.    The ability to  select and analyse the appropriate interest rate model. 3.    The ability to derive the prices and the hedging strategies of various financial derivatives. 4.    The ability to read, understand and communicate research literature in the field of fixed-income markets. 5.    The ability to recognise potential research opportunities and research directions.

### Syllabus

Continuous-time financial market model: The financial market model; Equivalent martigale measures; Risk-neutral pricing ; Change of numeraire; The generalised Black-Scholes model: pricing and hedging contingent claims; The Greeks; Futures market; Currency markets.

The Bond market:  The term structure of interest rates; Bond pricing; Short rate models; The term structure equation; Extensions: multi-factor models

The Heath-Jarrow-Morton Methodology: The Heath-Jarrow-Morton model class; Forward risk-neutral martingale measures; Completeness; Gaussian HJM framework; Swaps; Caps.

Market models of LIBOR- and Swap rates:  LIBOR dynamics under the forward LIBOR measure; The spot LIBOR measure; Valuation of Caplets and Floorlets; The swap market model.

### Recommended Texts

Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

### Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

MATH365 MEASURE THEORY AND PROBABILITY; MATH101 Calculus I; MATH103 Introduction to Linear Algebra; MATH162 INTRODUCTION TO STATISTICS; MATH264 STATISTICAL THEORY AND METHODS II

### Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Final Assessment  90    50
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Class Test on campus, closed book  90    50