Unit

School Of Computing, Engineering And Mathematics

Mathematical FinanceWestern Sydney University Unit Code: 200024.2

Discipline: STATISTICS

Student Contribution Band: 2

Level: 3

Credit Points: 10

Co ordinator
Rehez Ahlip


Prerequisite
200026 Advanced Mathematics for Business OR 200030 Differential Equations

Teaching Periods
Nothing on offer.

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About this Unit
The first section of the unit covers the idea of hedging and pricing by arbitrage in the discrete-time setting of binary trees. The key probabilistic concepts of conditional expectation, martingales, change of measure and representation are introduced in a simple framework. The second (and main) part of the unit concentrates on classical Black-Scholes analysis, assuming a lognormal random walk for asset prices. Ito's lemma and simple arbitrage arguments are used to derive the Black-Scholes partial differential equation for the fair value of an option. A variety of different kinds of options are considered and it is shown how, by suitably selecting boundary and final conditions for the Black-Scholes equation, virtually all derivative securities may be valued in a Black-Scholes framework. The unit concludes with a variety of 'exotic options': digital, pay-later, gap options and American options and the free boundary value problems. The link between the existence of equivalent martingale measures and the ability to price and hedge is formalised.


Courses
2739.2Bachelor of Business and CommerceCONTINUING
2739.5Bachelor of Business and CommerceCONTINUING
2753.1Bachelor of Business and CommerceCONTINUING


Specialisations

KT2006.1Financial MathematicsCONTINUING
M2016.1Applied MathematicsCONTINUING
SM2005.1Financial MathematicsCONTINUING




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