CASE STUDIES IN FINANCIAL MODELING, Fall 2007

Course Number: G63.2754

Instructors:
Jim Gatheral
Fellow of the Master of Science Program in Mathematics in Finance and Managing Director, Merrill Lynch & Co.,

Nassim Nicholas Taleb
Fellow of the Master of Science Program in Mathematics in Finance, Dean's Professor in the Sciences of Uncertainty, University of Massachusetts, Amherst, Professor of Marketing and co-director of the Decision Science Laboratory, London Business School.

Teaching Assistant:
Yevgeny (Gene) Vilensky
Courant Institute of Mathematical Sciences, Room 1109 WWH, vilensky@cims.nyu.edu. Office hours will be 5:30-6:30pm on Mondays.

The formal prerequisites for the course are Stochastic Calculus, Computing in Finance, and Continuous Time Finance. Students in the course will be expected to attend lectures, read the assigned material and do the assignments. Many of the assignments will be computational in nature. For these, students will be expected to use Matlab, R or C.

Note that there will be no exam! 80% of the final grade will be based on the written assignments, the remaining 20% on participation in class.

Official text: (essential for Jim Gatheral's part of the course) from Amazon: The Volatility Surface: A Practitioner's Guide or from Barnes and Noble with same-day delivery in Manhattan: The Volatility Surface: A Practitioner's Guide.

"Readers familiar with my lecture notes will surely recognize the contents of this book. I hope that even aficionados of the notes will find something of extra value in the book. The material has been expanded; there are more and better figures; and there's now an index."

For Nassim Taleb's part of the course, see his blog on Wilmott.com.

Highly recommended: (for both Jim Gatheral and Nassim Taleb's parts of the course) from Amazon: Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management by Jean-Philippe Bouchaud and Marc Potters or from Barnes and Noble with same-day delivery in Manhattan: Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management.

Link to Blackboard : (NYU's e-Education platform) classes.nyu.edu

All TA announcements including homework hand-in instructions will be made via Blackboard.

Lecture schedule:

09/06/2007 Nassim Taleb, What is Black-Scholes-Merton About?

Reading:

The Illusion of Dynamic Replication by Emanuel Derman and Nassim Taleb

Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula by Nassim Taleb and Espen Gaarder Haug

09/13/2007 Nassim Taleb, Fat tails and Power Laws

09/20/2007 Jim Gatheral, Stylized Facts

Reading: "Empirical properties of asset returns: stylized facts and statistical issues" by Rama Cont, Quantitative Finance Volume 1 (2001) 223–236.

See also, Real-time Volatility Estimation Under Zero Intelligence by Jim G. This presentation has a list of references to other papers on high-frequency data analysis. Developments in Volatility Derivatives Pricing has an example of a two-timescale stochastic volatility model.

Lecture notes: A brief outline

Homework: (due 10/02/2007) Gatheral Homework 1. Find data for this assignment here. Read Chapters 1 and 2 of the Volatility Surface and send questions to jim_gatheral at msn.com.

09/27/2007 Jim Gatheral, Stochastic Volatility and Local Volatility

Homework: (due 10/16/2007) Note new extended due date!

Gatheral Homework 2. Download Monte Carlo code here. Read Chapters 3 and 4 of the Volatility Surface and send questions to jim_gatheral at msn.com.

10/04/2007 Jim Gatheral, The Volatility Surface

Homework: (due 10/30/2007) Note new extended due date!

Gatheral Homework 3. Read Chapters 5 and 6 of the Volatility Surface and send questions to jim_gatheral at msn.com.

10/11/2007 Nassim Taleb, Four problems with probability distributions

10/18/2007 Nassim Taleb

10/25/2007 Not to be missed special guest lecture: Espen Gaarder Haug (Author of The Complete Guide to Option Pricing Formulas) , Space-time Finance, Relativity Theory's Implications for Mathematical Finance.

11/01/2007 Jim Gatheral, Jumps and Applications

Homework: (due 11/13/2007) Read Chapters 7 and 8 of the Volatility Surface and send questions to jim_gatheral at msn.com.

11/08/2007 Jim Gatheral, Asymptotics and Dynamics of the Volatility Surface

Homework: (Now due 12/07/2007. Please note the extension!) Gatheral Homework 4. Read Chapters 9 and 10 of the Volatility Surface and send questions to jim_gatheral at msn.com.

11/15/2007 Nassim Taleb

11/29/2007 Nassim Taleb, Introduction to Behavioral Problems in Finance

12/06/2007 Jim Gatheral, Barrier and other exotic options

Homework: (due 12/18/2007) Gatheral Homework 5. Read Chapter 11 of the Volatility Surface and send questions to jim_gatheral at msn.com.

12/11/2007 Jim Gatheral, Volatility Derivatives

Note that this is the Thanksgiving make-up lecture and so is on a Tuesday. Room 1302 is unavailable that evening so the class has been moved to room WWH 109. Please make a note of it!