Badm650-86 (Math570-81) Financial Derivatives              Spring 2005


Daily Syllabus     Peter Greim's home page    MACS home page   Registrar's page   Citadel home page  
 
Class   Tu  5:45 – 8:30 p.m.  TH 315

P. Greim, Thompson 329, Tel. 953­5035, E­mail: peter.greim@citadel.edu
http:// macs.citadel.edu/~greimp

Office hours  are posted at my door and at myclass schedule  web page. You can read it as long as you are using a Citadel terminal. The class schedule will give you an idea which times might be available if you need to make an appointment. Evening hours are Tuesday after class and Monday night.

Content:

This course introduces the mathematical treatment of the pricing of financial derivatives (such as forwards, futures, put and call options, European and American, exotic options, interest rate derivatives), based on the simple principle of (no) arbitrage.

We will begin with conceptually simple discrete time steps (binomial trees) and then proceed to the computationally more elegant continuous-time treatment (Brownian motion; Black-Scholes formula). Models will be applied to actual market data, using spreadsheets for the computations.

 

I will use MathCad for class demonstrations; it is useful for most of the homework problems, but not necessary. It is available in computer labs in Thompson Hall (220) and LeTellier Hall (203). You may also use Derive (on the Novell network) and Scientific Notebook (in GR 126 and TH 220). If you prefer to use your own software, you may do so.

Occasionally I will use Mathematica for symbolic computations that are too advanced or tedious – you will be able to read the corresponding files with the free Mathematica Reader (installed in TH215 and 220).

 

Prerequisites:

Calculus and basic notions of probability, such as expected value, standard deviation, conditional probability, independence, probability distributions, normal distribution. I will give a review of  facts in probability and statistics when needed.

 


Literature:

 

The first five of the following texts are on reserve in the Daniel library. I’ll base most lectures on #1 and #6.

 

1. Robert Jarrow and Stuart Turnbull: Derivative Securities, 2nd ed., South-Western, 2000. ISBN/ISSN: 0-538-87740-5 http://www.swcollege.com/finance/jarrow/jarrow.html There are only a few (70 or less) copies available from the publisher; the website is now obsolete. Jarrow/Turnbull contains lots of practical information, examples, and problems. The authors present the necessary mathematics in a way that you may be used to from business calculus courses.

 

2.  John C. Hull: Options, Futures, and Other Derivatives, 5th ed., Prentice-Hall, 2002. ISBN: 0-13-009056-5  http://vig.prenhall.com/catalog/academic/discipline/1,4094,237,00.html

Similar to Jarrow/Turnbull, even more praxis-oriented.

 

3. Neill A. Chriss:: Black-Scholes and Beyond: Option Pricing Models. McGraw-Hill, 1997. ISBN 0-786-31025-1http://catalogs.mhhe.com/mhhe/viewProductDetails.do?isbn=0786310251

(Virtually no mathematical prerequisites.)

 

4. Paul Wilmott, Sam Howison, Jeff Dewynne: The Mathematics of Financial Derivatives. Cambridge University Press, 1995. ISBN 0521497892   http://www.amazon.com/exec/obidos/ISBN%3D0521497892/103-7151271-0952661

 

5. Tomas Björk: Arbitrage Theory in Continuous Time. Oxford University Press, 1998. ISBN 0-19-877518-0  http://www.oup.co.uk/isbn/0-19-877518-0. This is the text on reserve in the library. There is an expanded second edition – see http://www.oup.co.uk/isbn/0-19-927126-7 .

Both Wilmott et al. and Björk concentrate on the underlying mathematics.

 

6. Robert V. Kohn: Derivative Securities.

Unpublished Lecture Notes, locally on the Novell network .

 

7. Martin W. Baxter, Andrew J. O. Rennie: Financial Calculus. (An Introduction to Derivative Pricing.)  Cambridge University Press, 1996. ISBN: 0521552893. http://books.cambridge.org/0521552893.htm

Baxter/Rennie concentrate on the mathematical treatment more than on the practical aspects. Their book is short and very concise, but you may find it fun to read.

 

8. Pablo Koch Medina, Sandro Merino: Mathematical Finance and Probability. Birkhäuser,2003. ISBN: 3-7643-6921-3
http://www.springeronline.com/sgw/cda/frontpage/0,11855,4-40109-22-2201906-0,00.html

 

9. Jean-Philippe Bouchaud, Marc Potters: Theory of Financial Risk and Derivative Pricing. From Statistical Physics to Risk Management. Cambridge University Press, 2003. ISBN:0521819164

http://uk.cambridge.org/catalogue/catalogue.asp?isbn=0521819164

 

10.  Philip Hunt, Joanne Kennedy: Financial Derivatives in Theory and Practice. Wiley, 2004. ISBN: 0-470-86359-5 

http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470863595.html

 

11. Marek Capinski, Tomasz Zastawniak: Mathematics for Finance. An Introduction to Financial Engineering. Springer-Verlag, 2003 ISBN: 1-85233-330-8

http://www.springeronline.com/sgw/cda/frontpage/0,11855,4-40109-22-2096935-0,00.html

 

Grades:

Course work includes lectures, mandatory homework, voluntary student presentations, one test, and a final exam. Homework counts 40%, the test 25%, and the final exam 35%.

 

Syllabus:

 

The course material is organized as outlined in the attached course calendar. I’ll adjust the pace if necessary. The typical class will be split in three parts, with short breaks in between: review of last week’s topics and assigned problems, new material, practice.