Here are the links to the lecture notes and exercises. They are in portable document format (pdf). You do not need to zip the files, since they are already compiled using the highest compress level. My notes are available for free for students and faculty of Goethe-University upon request. If you have not registered in class, please email me. You can also order a complete and revised set of my computational finance lecture notes on CD ROM. A folder with copies of the lecture notes is available at the library of the department of mathematics, Robert-Mayer-Strasse 8, 4th floor.

Contents

1. Introduction to Mathematical Finance
2. Newton's Method and its Application: A VolRetriever. The Excel spreadsheet is here.
3. Vanilla Options - Properties of the Black-Scholes formula
4. Volatility Management - Historic versus implied volatility, market data, smile reasons and shapes, risk reversals and butterflies, wing shifts
5. Normal Distribution and Characteristic Function: Plackett's Identity for Hessian and Correlation - Inversion Theorem by Gil-Paleaz
6. Efficient Computation of Option Price Sensitivities using Homogeneity and other Tricks
7. Numerical Integration and its Application to Spread Options: Midpoint Rule, Trapezoidal Rule, Simpson's Rule, Gaussian Quadrature. The Excel spreadsheet is here. There is also C source code and an executable in the front office section.
8. Fourier Transforms and their application to pricing path-independent multi-asset options, principal component transformation of the Black-Scholes partial differential equation
9. Binomial Trees in two dimensions and their application to options on the minimum/maximum of two assets. The Excel spreadsheet is here. Further FORTRAN source code is in the front office section
10. Termstructure Models and their Application, guest lecture by Dr. Ingo Schneider.
11. The Heat Equation
12. Finite Difference Methods
13. Survey on Barrier Options. The presentation on Ensuring Efficient Hedging of Barrier Options is at the section on conference talks.
14. Exercises

Literature

• Steven E. Shreve: Stochastic Calculus and Finance, lecture notes, Carnegie Mellon University, 1997. This is available for free at http://www.cs.cmu.edu/~chal/shreve.html.
• Hull: Options, Futures and other Derivatives, Prentice Hall, 1999.
• R. Seydel, Numerische Berechnung von Finanzderivaten, Springer, 2000.
• W. Shaw, Modelling Financial Derivatives with Mathematica, Cambridge.
• Wilmott; Derivatives, Wiley, 1998.