Module MA3481: Mathematical economics I

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2013-14
Contact Hours
11 weeks, 3 lectures including tutorials per week
Lecturer
Dr Silvia CalĂ˛
Learning Outcomes
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
Module Content
• Futures markets;
• Interest rates;
• Determination of Forward and Futures prices;
• Interest rate Futures;
• Introduction to options;
• Binomial Trees;
• 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 Greeks
Module Prerequisite
None
Required Textbook
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.

Assessment Detail
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.