Module Specification

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.
1. Module Title Financial Mathematics
2. Module Code MATH260
3. Year Session 2023-24
4. Originating Department Mathematical Sciences
5. Faculty Fac of Science & Engineering
6. Semester Second Semester
7. CATS Level Level 5 FHEQ
8. CATS Value 15
9. Member of staff with responsibility for the module
Dr SA Fairfax Mathematical Sciences Simon.Fairfax@liverpool.ac.uk
10. Module Moderator
11. Other Contributing Departments  
12. Other Staff Teaching on this Module
Dr R Zeineddine Mathematical Sciences Raghid.Zeineddine@liverpool.ac.uk
13. Board of Studies
14. Mode of Delivery
15. Location Main Liverpool City Campus
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
16. Study Hours 36

  12

      48
17.

Private Study

102
18.

TOTAL HOURS

150
 
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other
19. Timetable (if known)            
 
20. Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

MATH101 Calculus I; MATH103 Introduction to Linear Algebra; MATH102 CALCULUS II; MATH162 INTRODUCTION TO STATISTICS
21. Modules for which this module is a pre-requisite:

 
22. Co-requisite modules:

 
23. Linked Modules:

 
24. Programme(s) (including Year of Study) to which this module is available on a mandatory basis:

25. Programme(s) (including Year of Study) to which this module is available on a required basis:

26. Programme(s) (including Year of Study) to which this module is available on an optional basis:

27. Aims
 

To provide an understanding of basic theories in Financial Mathematics used in the study process of actuarial/financial interest.

To provide an introduction to financial methods and derivative pricing financial instruments in discrete time set up.

 
28. Learning Outcomes
 

(LO1) Know how to optimise portfolios and calculating risks associated with investment.

 

(LO2) Demonstrate principles of markets.

 

(LO3) Assess risks and rewards of financial products.

 

(LO4) Understand mathematical principles used for describing financial markets.

 
29. Teaching and Learning Strategies
 

Material is provided in advance of classes for students to study asynchronously. The contact hours consist of one 2-hour active learning session and one 2-hour supported study/drop-in session.

 
30. Syllabus
   

(a) Modern portfolio theory Introduce the Capital Asset Pricing Model and the uses of the CAMP, the capital market line and security market line, introduce and derive the formula for the Arbitrage Pricing Theory model.

(b) Introduction to markets and options Introduction to the concept of forward contracts, over‐the counter and exchange‐traded derivatives, use in hedging. Options: basics, strategies and profit diagrams, European and American options, put‐call parity.

(c) Discrete time Finance The concept of arbitrage free pricing (cash‐and‐carry pricing) will be explained and developed into the fundamental theorem of asset pricing in discrete time, the fundamental properties of option prices, no‐arbitrage pricing, the risk‐neutral probability measure and incomplete markets, pricing European‐style derivative contracts using binary trees and the binomial model, American options using the binomial model, random walk of asset pricing, the binomial model for stock prices and the Cox‐Ross‐Rubensein model.

(d) Continuous time finance Introduction to the concept of diffusion equations and their boundary conditions, the Brownian motion and its properties, calibration of the Binomial model as an approximation to Brownian motion, the Ito's formula (for pricing options), the Black‐Scholes formula, extend the Black‐Scholes formula to foreign currencies and dividend paying stocks, introduce the Greeks in portfolio risk management (Delta hedging, Delta of European stock options, Theta -- time decay of the portfolio, the Gamma).

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

Assessment

32. EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
  Final assessment 90 40
33. CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
  Group project requiring a written report with findings and a digital story summary 0 30
  Class test open book and remote (Moebius) 90 30