Instructor: Prof. Fotios C. Harmantzis
fharmant at stevens dot edu
 http://www.stevens.edu/fina

Teaching Assistants: Ms. Linyan Miao (Ph.D. Student)

Course Description

Obtain essential computational tools used in the industry by modern financial quantitative analysts. Become familiar with such methods as regression, time series analysis, decision methods, and simulation. Apply your results to forecasting, involving asset pricing, hedging, portfolio and risk assessment, investment strategies, and other financial problems. Become expert at using the latest software.

Students must have a strong mathematical background and be familiar with derivatives terminology and concepts at the level of Hull 's textbook. Each section of the course will cover theory and test your knowledge on developing models.

Prerequisites: Stochastic Calculus, Pricing and Hedging

Requirements: Assignments require knowledge of one of the following programming languages: C++/C#, VBA, Java.

Text Books

• Clewlow and Strickland. Implementing Derivatives Models . 1998. Wiley. ISBN: 0471966517
• Daniel J. Duffy. Financial Instrument Pricing using C++ . 2004. Wiley. ISBN: 0470855096

Grading

• Homework Assignments                          100%

Note:
Programming experience with a high-level language is essential for this course. The course will require a serious investment of time and effort. Do not take this course unless you feel comfortable with programming and you are prepared for a very substantial commitment.

Topics

1. Options Pricing & Hedging
• Binomial Trees. Trinomial Trees. Finite Difference Methods.
• Monte Carlo (MC) Simulations.
• Pricing via Fast Fourier Transform (FFT)
2. Exotic Derivatives
• Path Dependent Options. Barrier Options. Look-back Options. Asian Options
3. Credit Derivatives
• Pricing of CDS & CDOs, with/without simulation
4. Advanced Diffusion Models & Volatility Models
• Jump Diffusion Processes: Applications to Exotics and Default Models
• Variance Gamma Process
• Heston Model
5. Correlations Modeling
• Model Default correlations. Use of Copulas (Normal and other copulas)

Recommended Books

• London . Modeling Derivatives in C++ . 2004. Wiley. ISBN: 0471654647
• Benninga. Financial Modeling . Second Edition. 2000. The MIT Press. ISBN: 0262024829
• Mark Joshi. C++ Design Patterns and Derivatives Pricing. Cambridge . ISBN: 0521832357
• Paul Glasserman, Monte Carlo Methods in Financial Engineering (Stochastic Modelling and Applied Probability). 2004. Springer. ISBN 0-387-00451-3

Recommended Readings

• 2002, CreditGrades Technical Document, Technical Document, RiskMetrics Group, Inc.
• Carr, P. and L. Wu (2003): "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, 58, 753-777.
• Carr, P. and D. Madan (1998), "Option valuation using the FFT", Journal of Computational Finance, 2, 61-73.
• Hirsa, A. and D. B. Madan (2003), Pricing American options under Variance Gamma. Journal of Computational Finance, 7(2).
• Li, D. (2000), On default correlation: a copula function approach, Journal of Fixed Income, vol. 9(4) p. 43-54.
• Zhou, C. (2001), The Term Structure of Credit Spreads with Jump Risk, Journal of Banking and Finance, 25, 2015-40.

Recommended Sites for Programming Resources

Java:
• http://java.sun.com/j2se/1.4.2/download.html
• http://java.sun.com/j2se/1.5.0/download.jsp
• http://java.sun.com/docs/books/tutorial/index.html
• http://java.sun.com/docs/books/effective/
• http://www.developer.com/java/other/article.php/3112301
• http://www.cs.wisc.edu/~hasti/cs368/JavaTutorial/
• http://www.mathtools.net/Java/Finance_and_Economics/index.html

C++:
• http://www.mindview.net/Books/TICPP/ThinkingInCPP2e.html
• http://www.brpreiss.com/books/opus4/html/book.html
• http://library.lanl.gov/numerical/bookcpdf.html

C#:
• http://lab.msdn.microsoft.com/express/vcsharp/default.aspx
• http://www.softsteel.co.uk/tutorials/cSharp/cIndex.html
• http://csharpcomputing.com/Tutorials/TOC.htm