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

Teaching Assistants:

Mrs. Linyan Miao (PhD Student)

Course Description

Introduces you to basic financial derivatives theory and modeling, arbitrage, hedging, and risk. Acquire a serious grounding in theory, reviewing Ito's lemma, the diffusion equation, partial differential equations, and the Black-Scholes model and formulae. Learn how to estimate the volatility of historic data. Apply asset price random walks and log-normal distribution. Practical examples, based on numerical techniques, such as finite difference and binomial methods, are exploited to value options. Perform modeling and analysis drawn from financial information and software available on the internet.

Prerequisites: Probability and Stochastic Calculus

Requirements: Project requires knowledge of one of the following programming languages: C++, VBA, Java, or C#.Net.

Text Books

• Hull. Options, Futures, and Other Derivatives.  2005. Sixth Edition. Prentice Hall.  ISBN: 0131499084

Grading

• Homework Assignments (4 Sets)       20%

• Project                                                    15% 

• Final Exam                                              65%

Topics

• Introduction to Financial Derivatives

• Futures and Forwards

• Fixed Income: Interest Rates, Duration, Convexity, Swaps

• Options: Markets, Properties, Trading

• Discrete Time: Binomial Trees

• Continuous Times:  Stochastic Differential Equations, Ito, Black-Scholes

• Volatility Smiles

• “Greeks”

• Exotic Options

Selected Past Projects

• Optimal Technical Indicator in Matlab (P. Huang), 2006.
• The "FE620 Calculator" in C++/VB  (S. Gavnoudias), 2006.
• Valuation and Simulation of Credit Default Swaps (CDSs) in Java (L. Rodney), 2005.
• Default Correlations and CDO Tranches (A. Mehta), 2005.
• Implement a barrier model to estimate credit defaults, in VBA (R. Colavecchio), 2004.
• Implied Binomial Trees from Historical Distribution (S&P500 historical options prices) (K. Moh), 2005.
• Bond Options pricing and calibration using the Black-Derman-Toy term structure model, in VBA (L. Ortega), 2004.
• Implement Lookback Options in VBA as described in: Goldman, Sossin and Gatto’s 1979 paper “Path dependent options: buy at the low sell at the high”. (C. Gnafakis), 2004
• Value-at-Risk Measurement in C++: Historical vs. Simulation (G. Roy), 2004.
• Options Pricing and Implied Vols Modeling, in C#.Net (F. Lu), 2005.
• Options Pricing using Trinomial Trees in C++ (M. Krause), 2005.
• Options Pricing using Binomial Trees and Monte Carlo Simulation, in VBA (J. Murray), 2004.
• Options Pricing using Binomial Trees, in C++ (Y. Xiong), 2003.

Recommended Texts

• S. Neftci. Principles of Financial Engineering, 2004, Academic Press, ISBN: 0125153945
• S. Neftci. An Introduction to the Mathematics of Financial Derivatives, 2000, Academic Press, ISBN: 0125153929
• M. Baxter and A. Rennie. Financial Calculus: An Introduction to Derivative Pricing, 1996,  Cambridge Univ. Press, ISBN  0-52-155289-3
• P. Wilmott, S. Howison and J. Dewynne. The Mathematics of Financial Derivatives:  A student introduction, 1995, Cambridge Univ. Press, ISBN 0-52-149789-2
• Wilmott. Paul Wilmott on Quantitative Finance. Wiley. 2000. ISBN: 0471874388
• Duffie. Dynamic Asset Pricing Theory, Princeton Univ. Press, 3rd Edition, ISBN: 069109022X