Probability and Statistics in Complex Systems: Genomics, Networks, and Financial Engineering, September 1, 2003 - June 30, 2004

Spring 2004

IMA Workshop 7:

Risk Management and Model Specifications Issues in Finance

April 12-16, 2004

Organizers:

Marco Avellaneda
Courant Institute of Mathematical Sciences
New York University
avellane@cims.nyu.edu
http://www.math.nyu.edu/faculty/avellane/

and

Rama CONT
Centre de Mathématiques Appliquées
École Polytechnique
Rama.Cont@polytechnique.fr
http://www.cmap.polytechnique.fr/~rama/

Schedule	Participants	Registration	Feedback
Abstracts
Material from Talks
Photo Gallery

Some of the most interesting themes in quantitative finance and econometrics have to do with model specification in the broadest sense, including the statistical analysis of market data from multi-asset, multi-currency markets with a high number of state variables but also indirect identification of models from option prices ("model calibration"). The statistical analysis of the distribution of returns often requires advanced techniques, such as nonlinear regression (ARCH/GARCH), nonstationary modeling of time series (to take into account seasonal effects), neural networks and data-mining. In addition to the statistical analysis of multivariate returns, quantitative modeling is also concerned with derivatives and relative-value analysis, which require working with so-called "risk-adjusted" probability distributions. In fact, prices observed at any given time contain "forward looking" information about future cash flows in the form of market prices of traded options.

This means that the models that are used to price and hedge derivatives must be determined partially from econometric information and partially by solving "inverse problems" (in the sense of going from prices to parameters) that reflect current market prices. Inverse problems in asset-pricing theory comprise diverse questions in finance, such as the construction of smooth forward rate curves from interest rate futures, swaps and bond price data, the calculation of "volatility surfaces" from observation of option prices and more generally implying parameters of more complex models from observed option prices. These inverse problems are ill-posed, i.e., exhibit sensitive dependence to input data. This workshop will be centered on robust techniques and algorithms for solving such problems in different market contexts (e.g., fixed income/capital markets derivatives, credit derivatives, commodities market models, etc.), their theoretical foundations, their economic interpretation and the interplay of model identification problems with risk management issues.

Mathematical Areas of Relevance:

Stochastic differential equations
Markov Processes
Ill-posed inverse problems and regularization methods
Linear and nonlinear Partial Differential Equations
Optimization: dynamic programming, duality techniques, semidefinite programming
Duality methods in optimization
Mathematics of information theory
Parametric and nonparametric statistics
Numerical methods and their implementation

WORKSHOP SCHEDULE

MONDAY, APRIL 12
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.

8:30

Coffee and Registration

Reception Room EE/CS 3-176

9:15

Douglas N. Arnold, Scot Adams, and Organizers

Welcome and Introduction

9:30

Marco Avellaneda
New York University

A Market-Induced Mechanism for Stock Pinning on Option Expiration Dates

Slides: PinningSlides.pdf
Paper: qf3601.pdf

10:20

Discussion

10:30

Coffee Break

Reception Room EE/CS 3-176

11:00

Alexandre d'Aspremont
University of California, Berkeley

A Moment Approach to the Static Arbitrage Problem on Baskets

Slides: pdf

11:50

Discussion

12:00

Lunch Break

1:30

Thaleia Zariphopoulou
University of Texas at Austin

Optimal Investments in Markets with Stochastic Opportunity Sets

Slides: zariphopoulou1.pdf
zariphopoulou2.pdf