SIAM Short Course on
An Introduction to Optimization in Finance

Sunday, May 9
Sheraton Spirit of Atlanta Hotel, Atlanta, Georgia

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Organizers and Instructors

Thomas F. Coleman, Cornell University
Ron S. Dembo, Algorithmics, Inc.

Rationale

Computational finance is a field experiencing dramatic growth in importance and popularity. Moreover, any important finance strategy questions can be phrased as optimization questions.

Course Description

The purpose of this course is to illustrate and describe the role of optimization in computational finance. Finance concepts will be introduced and defined as required. It is assumed that the course participants have some awareness of optimization methods and problems, particularly linear and quadratic programming.

The discussion in the morning will be devoted to portfolio analysis. We will discuss an idea that has set the tone for most of the portfolio selection/modification strategies, the Markowitz "efficient frontier". This idea leads to the formulation and solution of quadratic programming problems -- we will examine this in detail. Despite the great popularity and success of this idea, there are some problems. In particular, the Markowitz efficient frontier rests on certain assumptions - liquidity and smoothness, which are often violated in practise. Therefore, the second half of the morning discussion will consider relaxing some of these assumptions. The result is a "downside minimization" approach that ultimately yields linear programming problems.

In the afternoon we will turn to the important question of pricing and hedging financial derivatives. This is a rich and deep topic requiring much more than an afternoon to cover with any rigor. Nevertheless, we will introduce this topic highlighting issues that involve optimization. For example, a fundamental approach to the pricing and hedging of derivatives involves the famous Black-Scholes (and generalized Black-Scholes) equation. (We will introduce this equation in class). However, in order to use the equation in practise a parameter, the volatility, must be computed. We will discuss this computation from an optimization perspective.

We conclude the afternoon discussion by observing that dynamic hedging strategies based on Black-Scholes replication are well-suited to portfolio replication in efficient, frictionless markets that operate continuously. However, in practise markets exhibit jumps where the execution of this B-S strategy becomes expensive, perhaps impossible. We discuss an alternate ''scenario-based'' approach, solved via optimization, that can efficiently handle market jumps and discontinuities.

Course Objectives

The main objective of this course is to illustrate the historical, current, and growing role of practical optimization ideas in computational finance.The emphasis is on practical computational aspects. A secondary objective is to introduce attendees with optimization background or interest to the area of computational finance.

Level of Material

From a financial mathematics perspective 80% of the course will be introductory with 20% intermediate or advanced. Almost all finance concepts will be introduced from the basics, assuming no previous knowledge. The optimization level required will be about 40% introductory, 40% intermediate, and 20% advanced.

Prospective Attendees

We expect the course participants to come from both academia and industry with some background/interest in practical optimization. We expect little specific background in finance. In particular, many firms that do mathematical finance hire quantitative analysts with a technical background, but with little exposure to the specific computational aspects of finance. This course should be ideal for such people to gain exposure to the computational optimization side of finance. This course should also appeal to academics in operations research, applied mathematics, or computer science.

Recommended Background

Undergraduate training in mathematics, applied mathematics, operations research, or computer science. Some familiarity with numerical methods and techniques. Exposure to numerical methods for optimization, especially linear and quadratic programming.

The Instructors

Thomas F. Coleman

is a Professor of Computer Science and Director of two Cornell research centers: the Cornell Theory Center (a supercomputer center), and the Center for Applied Mathematics. Coleman is Chair of the SIAM Activity Group on Optimization (1998-2001) and is on the editorial board of several journals: the SIAM Journal on Scientific Computing, Applied Mathematics Letters, and Computational Optimization and Applications (Kluwer). He is author of two books on computational mathematics, editor of four proceedings, and has published over fifty technical articles. Coleman is a Mathworks, Inc. consultant. Coleman's main research interest is the study of algorithms for numerical optimization with emphasis on large-scale problems and applications, especially as applied to finance. Coleman has established the Computational Finance Institute, a finance computing/research organization within the Cornell Theory Center, with a consulting/research/training office in New York City.

Ron S. Dembo

is President and CEO of Algorithmics Incorporated, a leading provider of enterprise-wide financial risk management software, which he founded in 1989. Before founding Algorithmics, Dembo created and managed a group at Goldman Sachs responsible for fixed income optimization modelling. Prior to that Dembo was a faculty member at Yale University in Operations Research. Dembo has written and published over 50 technical papers on finance and mathematical optimization and holds two trademark patents for portfolio replication. Currently, he is an adjunct Professor for Operations Research at the University of Toronto. Dembo is also founder of NetExposure, an Electronic Journal of Financial Risk.

Program

Morning

8:00 Registration

8:30 - 10:00 Portfolio Analysis

  • Markowitz and the Efficient Frontier

10:00 - 10:30 Coffee

10:30 12:00 Portfolio Analysis (continued)

  • Liquid Markets, Downside Minimization, Risk-Adjusted Returns

Afternoon

12:00 - 2:00 Lunch

2:00 - 3:30 Valuation of Derivatives and Hedging

  • Black-Scholes and Generalized Black-Scholes, Implied Volatility Surfaces

3:30 - 4:00 Coffee

4:00 - 5:30 Valuation of Derivatives and Hedging (continued)

  • Hedging in Markets that Gap

5:30 Short Course adjourns

Registration

Seats are limited. We urge attendees to register in advance. To register for either short course, please complete the online Preregistration Form and submit to SIAM. Registration fee for the course includes course notes, coffee breaks, and lunch on Sunday, May 9.

Location

This short course will be in Atlanta 2. The coffee breaks will be in Convention Lobby; lunch will be in Capitol South.

MMDCreated: 12/21/98 Updated: 12/21/98