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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 Calò
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.
 
Additional Reading
  • 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.