Modern financial markets are marked by the widespread prevalence of new financial products, the importance of risk management, and the availability of powerful computational technology. In this class, we develop financial models and computational methods to solve pricing, hedging, and portfolio optimization problems that appear everyday in financial markets. The emphasis is on a practical approach: we apply models and methods in a hands-on fashion to real problems, and simultaneously highlight their limitations in real situations. We develop techniques to price a wide array of equity derivatives, including path-dependent options and multi-asset options. We explore the related problems of hedging and risk management, and we address issues that arise in short and long term portfolio optimization. We construct models for the evolution of interest rates, to allow for the pricing and hedging of interest rate derivatives. Finally, we discuss models for credit sensitive securities.
This course assumes a working knowledge of statistics (at the level of the B6014 Statistics course) and optimization and simulation (at the level of the B6015 Decision Models course). Students must also be familiar with basic options concepts (at the level of the B8311 Options Markets course) and fixed income concepts (at the level of the B8308 Debt Markets course). Students must also be proficient in Excel, the use of the Solver (Excel’s built-in optimizer), and Crystal Ball for spreadsheet simulation. This course is intended to be complementary to the B8312 Advanced Derivatives course.
A good review for the course would be to read or reread chapters 1–12 of Hull’s textbook: • J. C. Hull, Options, Futures, and Other Derivatives, 6th Edition. Prentice Hall, 2005. Non-MBA students must be able to program in Visual Basic in order to complete the homework assignments and final exam. For links to free VBA books, use the Columbia Library Books 24x7:
Follow this link, click “Connect” and login with your UNI. Then, select “View by: IT and Technical Topics”, then “Programming Languages”, and then “Visual Basic”. Alternatively, a very good book on VBA is: • S. C. Albright, VBA for Modelers: Developing Decision Support Systems Using Microsoft Excel, 2nd Edition. South-Western College Publishers, 2006.
Ziv Katalan was a Columbia Business School faculty member from to 2016.