### 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 MATL481 Coordinator Dr S Mitra Mathematical Sciences Sovan.Mitra@liverpool.ac.uk Year CATS Level Semester CATS Value Session 2019-20 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 o fbasic fixed-income securities,  such as bonds, swaps, caps,  swapations, caplets, and floorlets.

### Learning Outcomes

(LO1) A critical awareness of current problems and research issues in thefield of financial derivatives, interest rate models, and fixed-incomesecurities.

(LO2) The ability to select and analyse the appropriate interest rate model.

(LO3) The ability to derive the prices and the hedging strategies of variousfinancial derivatives.

(LO4) The ability to read, understand andcommunicate research literature in the field of fixed-income markets.

(LO5) The ability to recognise potential research opportunities and researchdirections.

(S1) Problem solving skills

(S2) Numeracy

### Syllabus

Continuous-time financial market model: The financial market model; Equivalent martigale measures; Risk-neutralpricing ; 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 martingalemeasures; Completeness; Gaussian HJM framework; Swaps; Caps. Market models of LIBOR- andSwap rates:  LIBOR dynamics under the forward LIBOR measure; The spot LIBOR measure;Valuation of Caplets and Floorlets; The swap market model

### Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Exam There is a resit opportunity. Standard UoL penalty applies for late submission. This is an anonymous assessment. Assessment Schedule (When) :End of Semester  150 minutes.    90
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Regular problem sets Standard UoL penalty applies for late submission. This is not an anonymous assessment. Assessment Schedule (When) :During the semester      10