On successful completion of this module, students will be able to:
Describe the characteristics and categorise the uses of a wide variety of financial options, futures and derivatives;
Quantify the prices of various financial options and futures;
Demonstrate the precise mathematical detail of the definition and construction of the Ito integral and assess its uses;
Explain the Black-Scholes methodaology, construct its PDE, and illustrate its application in deriving option prices in continuous time models.
Explain and appraise the differenct measures for calculating the sensitivity of derivative prices to underlying conditions
Determination of Forward and Futures prices;
Interest rate Futures;
Introduction to options;
An introduction to stochastic calculus; a)Wiener Processes and Brownian Motion b) How stochastic calculus differs from standard calculus c) Taylor series expansion
Derivation of Ito's Lemma
Black Scholes Merton of method of derivative pricing
The required text book is John C.Hull's 'Options, Futures and Other Derivatives', published by Pearson Prentice-Hall. Any edition will do but the seventh edition is preferable. there will be exercises set from this text book throughout the module so students will be at a significant disadvantag if they do not have a copy of this text.
There are numerous copies of this textbook in the Lecky Library. This is a fairly basic textbook but deals with the essentials well. It will be supplemented by lecture notes and handouts throughout the course.
Cvitani\'c, J & Zapatero, F.(2004), An Introduction to the Economics and Mathematics of Financial Markets, MIT press.
Neftci, S., (2000), An Introduction to the Mathematics of Financial Derivatives, Academic Press.
Steele, M.J. (2000), Stochastic Calculus and Financial Applications, Springer.
Karatzas, I. and Shreve, S. (1991), Methods of Mathematical Finance, Springer.
Dumas, B. & Allaz B. (1995), Financial Securities: Market Equilibrium and Pricing Methods, Chapman and Hall.
Nielsen, L.T. (1999), Pricing and Hedging of Derivative Securities, Oxford University Press
Higham, D.J. (2004), An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, Cambridge University Press
Brzezniak, Z & Zastawniak, T (1999), Basic Stochastic Processes: A Course Through Exercises, Springer.
This module will be examined
in a 2-hour examination in Trinity term.
There will be
one term test in Michaelmas term which will be worth 10% of the final grade. If a supplemental exam is required, it will consist of 100% exam.