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

200026 Advanced Mathematics for Business OR 200030 Differential Equations

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.

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