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 Financial Mathematics
Code MATH260
Coordinator Dr SA Fairfax
Mathematical Sciences
Simon.Fairfax@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2021-22 Level 5 FHEQ Second Semester 15

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.

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.

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).

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):
MATH102 CALCULUS II; MATH101 Calculus I; MATH103 Introduction to Linear Algebra; MATH162 INTRODUCTION TO STATISTICS 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

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

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

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
final assessment on campus  60 minutes    40       
Class test open book and remote  90 minutes    30       
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  3 weeks on task    30