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

Spring 2004

IMA Short Course:

Tools for Modeling and Data Analysis in Finance/Asset Pricing

March 29-April 2, 2004

Schedule Participants Registration
IMA Public Lecture: Stephen Ross, Behavioral Finance - The Closed End Fund Puzzle, March 30, 2004
Talks(A/V)    Talks (Audio)
Photo Gallery
Slides:   html    pdf    ps    ppt

Topics covered: This tutorial recounts the state of the art in asset pricing theory and modeling. In many cases, models can be crucial for decision-making and the allocation of financial resources. Investment banks, often the most efficient users of capital, manage their trading portfolios using simulation models calibrated to hundreds of traded instruments. These models are used to price illiquid instruments as well as to manage the exposure of the firms to market and credit risk. The result is a more efficient use of economic capital and, hopefully, a more transparent relation between financial institutions and regulators. Leading theoreticians and practitioners will lecture on the models used in the main asset classes.

Speakers:

Blaise G. Morton
EBF Funds
blaise.morton@ebf.com

Glenn J. Satty
Telluride Asset Management
gsatty@tridecap.com

Srdjan D. Stojanovic
Department of Mathematical Sciences
University of Cincinnati
http://math.uc.edu/~srdjan/

Carlos Fabian Tolmasky
University of Minnesota
tolmasky@math.umn.edu

Syllabus:

Options Pricing, Portfolio Hedging, and Data Analysis
Lecturer: Srdjan D. Stojanovic

1. Classical methods in options pricing and hedging. European options. Traditional derivation of the Black-Scholes PDE. Monte-Carlo verification of the derivation. Black-Scholes formula and extensions for time dependent data. Effect of continuous and instantaneous dividends. Numerical extensions for price dependent data. American options, optimal stopping, and (obstacle) free boundary problems. Numerical solutions.

2. Options data analysis. Options data. Elementary implied volatility. Derivation of the Dupire PDE and integral-differential equations. Non- elementary methods for implied volatility, and other parameter estimation problems in complete markets: optimal control of Dupire PDEs, integral- differential equations, and obstacle problems.

3. Optimal portfolio hedging. Merton's classical optimal portfolio theory for (linear) Log-Normal markets. Portfolio hedging formula under appreciation rate uncertainty for linear non-Markovian markets. Portfolio hedging for multi-factor non-linear Markovian markets. Hamilton-Jacobi-Bellman and Monge-Ampère PDEs in optimal portfolio hedging. Portfolio hedging for multi- factor non-linear Markovian markets under general affine constraints on the portfolio.

4. State of the art in options pricing and hedging. Stochastic volatility models. Market price of volatility risk. The general problem of option pricing in incomplete Markovian markets. Complete solution of the general option pricing problem in incomplete Markovian markets via optimal portfolio theory, and Monge-Ampère PDEs. Unique fair prices. Non-unique fair prices: price-spread. Black-Scholes and optimal options hedging in general incomplete markets.

Preprints:
StojanovicPreprintPortfolioFormula.pdf
StojanovicPreprintStochasticVolatility.pdf
StojanovicPreprintHypoellipticBlackScholes.pdf

Practical Aspects of Risk, Utility, and Derivative Valuation
Lecturer: Glenn J. Satty

1. Utility and Behavior: practical examples of why rational people behave differently whether or not they have the same information, and how utility and behavior impact financial markets and pricing of financial instruments.

2. Fundamental Intuition behind Derivative Pricing: reducing the Black-Scholes equation and its solution to a "trading intuitive" form, in order to understand how traders and risk controllers use the equations and formulae in their daily work.

3. Relationship between Γ and Θ: how a market maker risk manages a position in real time. In this section we discuss ways a market maker makes money on both short and long term positions. If time permits we will also discuss classical portfolio insurance and its effect on the market.

4. Topics on Demand: according to the group we can discuss other issues, including different dynamics in different markets, actual vs theoretical distributions, exotic options, or other topics of interest. If time permits we may have a mock trading session.

Derivatives in Commodity Markets
Lecturer: Carlos Fabian Tolmasky

1. Generalities. Consumption and non-consumption commodities. Storage. Arbitrage relationships. Convenience yield. Contango, backwardation. Seasonality. Futures and Swaps. Mechanics: exchange traded contracts, over-the-counter contracts. Basis risk. Hedging. Example: Metallgesellschaft.

2. Description of some market structures and participants: metals, grains, energy (petroleum, natural gas, electricity), weather.

3. More on Swaps. Vanilla Options on futures. Spread options: craks, crush and timespread options. Asian options and options on swaps.

4. Term structure models. One factor models. Stochastic convenience yield. Gibson and Schwartz model. Statistics of various futures and volatility curves. Multicurve markets, intra and inter curve correlations.

5. Petroleum market revisited: the market as a description of a refinery and its economics.

Slides:   Commod.pdf

Quantitative Methods for Pricing Fixed-Income Securities
Lecturer: Blaise G. Morton
(based on notes by Blaise Morton and Thomas Spiegel)

1. Introduction to Bonds and the Fixed-Income Markets. What is the market structure and who are the players. Basic models of Treasury Yield curves. Practical and philosophical issues with continuous yield curves. Back to reality with treasury, swap and agency dealer screens, quoting conventions. Treasury curve modeling techniques and basic analyses such as duration, convexity and the convexity bias. Understanding the shape of the treasury curve (following Ilmanen). A formula for expected bond return

2. Interest-Rate Swaps and the LIBOR Curve. Basic models. Building the LIBOR (rate) curve. Money market, interest-rate swaps and Eurodollar futures. The convexity bias in Eurodollar Futures (following Burghardt). The repo market -- Basic trades and determining fair value. Definitions of spread trading and fixed-income arbitrage.

3. Stochastic Models and Derivatives Pricing. Black's model applied to pricing interest-rate caps, floors. Binomial trees for pricing callable bonds using the option-adjusted spread (OAS). PDE pricing models based on stochastic differential equations, example: the first convertible bond model of Brennan and Schwartz. Market Models, example: swaption pricing.

SHORT COURSE SCHEDULE
Monday Tuesday
MONDAY, MARCH 29
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 and Scot Adams Welcome and Introduction
9:30-10:15 Part 1
10:15-10:30 Break Reception Room EE/CS 3-176
10:30-11:15 Part 2
11:15-1:30 Lunch break
1:30-2:15 Part 3
2:15-2:30 Break Reception Room EE/CS 3-176
2:30-3:15 Part 4
TUESDAY, MARCH 30
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:00 Coffee Reception Room EE/CS 3-176
Glenn J. Satty (Telluride Asset Management)
Practical Aspects of Risk, Utility, and Derivative Valuation
9:30-10:15 Part 1
10:15-10:30 Break Reception Room EE/CS 3-176
10:30-11:15 Part 2
11:15-1:30 Lunch break
1:30-2:15 Part 3
2:15-2:30 Break Reception Room EE/CS 3-176
2:30-3:15 Part 4
IMA Public Lecture
March 30, 2004 , Room 100 Smith Hall
5:00-6:30 pm Reception Lind Hall 400
7:00 pm
Room 100 Smith Hall
Stephen A. Ross
Massachusetts Institute of Technology

Behavioral Finance - The Closed End Fund Puzzle

Talks(A/V)    Talks (Audio)
Photo Gallery

Slides:   html    pdf    ps    ppt

WEDNESDAY, MARCH 31
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:00 Coffee Reception Room EE/CS 3-176

Carlos Fabian Tolmasky (University of Minnesota)
Derivatives in Commodity Markets

Slides:   Commod.pdf

9:30-10:15 Part 1
10:15-10:30 Break Reception Room EE/CS 3-176
10:30-11:15 Part 2
11:15-1:30 Lunch break
1:30-2:15 Part 3
2:15-2:30 Break Reception Room EE/CS 3-176
2:30-3:15 Part 4
THURSDAY, APRIL 1
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:00 Coffee Reception Room EE/CS 3-176
9:30-10:15 Part 1
10:15-10:30 Break Reception Room EE/CS 3-176
10:30-11:15 Part 2
11:15-1:30 Lunch break
1:30-2:15 Part 3
2:15-2:30 Break Reception Room EE/CS 3-176
2:30-3:15 Part 4
FRIDAY, APRIL 2
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:00 Coffee Reception Room EE/CS 3-176
9:30-10:15 Part 5
10:15-10:30 Break Reception Room EE/CS 3-176
10:30-11:15 Part 6
IMA/MCIM Industrial Problems Seminar
April 2, 2004 , EE/CS 3-180
1:25-2:15
Richard Derrig
(President, OPAL Consulting LLC, Visiting Scholar, Wharton School, University of Pennsylvania)

Mathematical Models for Insurance Fraud Detection

Paper: Fraud Classification Using Principal Component Analysis of RIDITs (pdf)

Monday Tuesday

LIST OF CONFIRMED PARTICIPANTS

Name Department Affiliation
Vilen Abramov Department of Mathematics Kent State University
Scot Adams Institute for Mathematics and its Applications University of Minnesota
Inkyung Ahn Department of Mathematics Korea University
Hengjie Ai Department of Economics University of Minnesota
Greg Anderson School of Mathematics University of Minnesota
Valentin Andreev Department of Mathematics Lamar University
Douglas N. Arnold Institute for Mathematics and its Applications University of Minnesota
Donald G. Aronson Institute for Mathematics and its Applications University of Minnesota
Sezai Ata School of Mathematics University of Minnesota
Gerard Awanou Institute for Mathematics and its Applications University of Minnesota
Hee-Jeong Baek Department of Mathematics Seoul National University (BK21)
Karen Ball   University of Minnesota
Antar Bandyopadhyay   University of Minnesota
Peter Bank Department of Mathematics Humboldt University of Berlin
Camelia Bejan Department of Economics University of Minnesota
Slava Belyaev   ITEP
Florin Bidian Department of Economics University of Minnesota
Hunt McCall Blatz Quantitative Group Advantus Capital Management
Maury Bramson Department of Mathematics University of Minnesota
Olga Brezhneva   University of Minnesota
James B. Carson   RisQuant Energy
Jamylle Carter Department of Mathematics University of Minnesota
Zhiwei Chen Department of Mathematics University of Maryland
Dong Myung Chung   Sogang University
Pin Johnny Chung Investment & Risk Management Chung ALM
Daya Dayananda Department of Mathematics University of St. Thomas
Richard Derrig   Opal Consulting LLC
Gregory S. Duane Institute of Applied Mathematics and Computer Science Technology University of Minnesota
Yang Fan Department of Statistics University of Minnesota
Narryn Fisher Department of Mathematics University of Maryland
Louis Forti Department of Energy Risk Trading CHS Inc.
Liliane Forzani Department of Statistics University of Minnesota
Shmuel Friedland Department of Mathematics University of Illinois - Chicago
Tim Garoni Institute for Mathematics and its Applications University of Minnesota
Urmi Ghosh-Dastidar Department of Mathematics City University of New York
Victor Goodman Department of Mathematics Indiana University
Elliot C. Gootman Department of Mathematics University of Georgia
Lawrence F. Gray School of Mathematics University of Minnesota
Matthew Gray   Allianz Life Insurance
Marshall Hampton School of Mathematics University of Minnesota
Chuan-Hsiang Han Ford Company University of Minnesota
Silvia Iorgova International Capital Markets Department International Monetary Fund
Naresh Jain School of Mathematics University of Minnesota
Abu Jalal Department of Finance University of Minnesota
Sung Chan Jun Department of Biological and Quantum Physics Los Alamos National Laboratory
Dhandapani Kannan Department of Mathematics University of Georgia
John Kemper Department of Mathematics University of St. Thomas
Mohammad Kazim Khan Department of Mathematics Kent State University
Andy Young Han Kim Department of Applied Economics University of Minnesota
Bong Soo Ko Department of Mathematics Education Cheju National University
Thomas G. Kurtz Department of Mathematics and Statistics University of Wisconsin
Chang Hyeong Lee Department of Mathematics University of Minnesota
Jeong Hyun Lee Department of Mathematics Seoul National University (SRCCS)
Rodrigo J. Lievano Department of FMIS University of Minnesota - Duluth
Mingyan Lin School of Mathematics University of Minnesota
Xiaoji Lin Department of Finance University of Minnesota
Dennis Lui Wells Capital Management Wells Fargo
Huaqiang Ma Department of Mathematics University of Maryland
Andy Mack Quantitative Finance Department Telluride Asset Management
Hantao Mai Department of Mathematics University of Maryland
Richard P. McGehee School of Mathematics University of Minnesota
Andreas Michlmayr   Patpatia & Associates
Oana Mocioalca Department of Mathematics Purdue University
Hamid Mohtadi Department of Applied Economics University of Minnesota
Blaise G. Morton   EBF & Associates
Gary Nan Tie   The St. Paul Companies
J. Michael Neal Department of Statistics University of Minnesota
Amir Niknejad Department of Mathematics University of Illinois - Chicago
Glenn Pederson Department of Applied Economics University of Minnesota
Thomas J. Peters Department of Computer Science University of Connecticut
Lea Popovic Institute for Mathematics and its Applications University of Minnesota
H. K. Pradhan Department of Finance and Economics XLRI Jamshedpur
Huiyan Qiu Finance Department University of Minnesota
Greg Rempala Department of Mathematics University of Louisville
Stephen Ross Sloan School of Management Massachusetts Institute of Technology
Fadil Santosa Institute for Mathematics and its Applications University of Minnesota
Glenn J. Satty   Telluride Asset Management
Arnd Scheel Institute for Mathematics and its Applications University of Minnesota
Jamie Seguino Corporate Economics Ford Motor Company
A. Christian Silva Department of Physics University of Maryland
Mihai Sirbu Department of Mathematical Sciences Carnegie Mellon University
Srdjan Stojanovic Department of Mathematical Sciences University of Cincinnati
Marcelo Yoshio Takami Department of Research Central Bank of Brazil
Peter Tankov Centre de Mathématiques Appliquées Ecole Polytechnique
Carlos Fabian Tolmasky   Cargill, Inc.
Pradyumna S. Upadrashta Department of Scientific Computation University of Minnesota
Hong Wang Department of Civil Engineering University of Minnesota
Jing Wang   University of Minnesota
Xiaodi Wang Department of Mathematics Western Connecticut State University
Yuhong Yang Department of Statistics Iowa State University
Ofer Zeitouni School of Mathematics University of Minnesota
Bing Zhang Department of Mathematics University of Maryland
Tao Zhang Department of Mathematics Purdue University
Yuming Zhang Department of Mathematics University of Maryland
Jun Zhao   University of Minnesota

 

IMA Public Lecture: Stephen Ross, Behavioral Finance - The Closed End Fund Puzzle, March 30, 2004

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