# Module MA3481: Mathematical Economics I

**Credit weighting (ECTS)**- 5 credits
**Semester/term taught**- Michaelmas term 2012-13
**Contact Hours**- 11 weeks. This module consists of 2 lectures and 1 tutorial per week. The tutorial sessions will be used to work through examples and problem sheets.
**Lecturer**- Prof. Eleanor Denny (Economics)
**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.

- Cvitani\'c, J & Zapatero, F.(2004),
**Assessment Detail**-
This module will be examined jointly with MA3482
in a 3-hour
**examination**in Trinity term, except that those taking just one of the two modules will have a 2 hour examination. However there will be separate results for MA3481 and MA3482. - There will be one term test in Michaelmas term which will be worth 10% of the final grade.