Finance 550 Numerical Methods & Optimization in Finance

Phil Dybvig
314-398-3196 (cell)

Washington University Olin School

Focus: Optimization tools that are useful in finance

Optimization is one of the pillars of finance that was inherited from Economics, and is a powerful tool that is used widely in practice. Many of the numerical tools were developed in Operations Research. We are limited in scope by the Mini format, but we will talk some about algorithms but mostly about tools and some applications.

Essential tools and concepts, up-to-date applications The tools we will discuss have been around a long time and I knew about most of them when I was in graduate school. However, most of the applications are newer and I had a part in developing some of them.

Prerequisites Introductory finance and a thorough knowledge of binomial option pricing are essential. Being in the quant track MSF program (or my permission) is the only formal prerequisite. As in most quantitative courses, students with the strongest math backgrounds will breeze through most easily.

Feedback Feedback is useful and appreciated. A good job of pointing out typos, conceptual problems, and other deficiencies of the course can increase your grade at the margin.

Organization of the course The course will be in a traditional lecture format, with problem sets and a final exam.

Course Requirements Grades will be based 70% on the final exam and 30% on the problem sets. Class participation may change a grade near a cutoff, as may useful feedback on the course materials. Understandably, job search or other obligations may occasionally conflict with class. It is your responsibility to find out from your classmates what you miss when you are absent.

Problem Sets The problem sets are available on my web page or through Blackboard (which also points at the web page). Problem sets have several parts. The normal parts without any special label are recommended for all students. Some will have solutions provided for study and learning, and the rest of the normal problems (and optionally "Extra for Experts" problems) should be submitted for grading. "Extra for Experts" problems are more difficult and are not required. The "Challengers" are very tough questions intended to stretch the very best students.

Rules for Problem Sets Students are permitted to get help from anyone for the normal and extra-for-experts parts of the homework, but students are required to do their own write-ups and any computer work individually. The challenger questions are strictly individual efforts. All homeworks and related programs should be handed in at the start of the following week's class.

Final Exam The final exam is scheduled on Thursday, December 13, 1:00-4:00, in Simon 106. Usually, my exams are straightforward and if you have done the homeworks yourself and you go to the lectures and study the slides you should do well. If you miss the exam for whatever reason or you need to take the exam at another time, I will substitute an oral exam. This avoids even the appearance that someone may have access to exam questions or answers in advance.

Course materials Course materials include slides and problem sets that are available on the web, and there are also books on reserve in the library that may be helpful. There is no separate packet.

Transparencies The lectures will be based on transparency slides that are available on the Web. You will probably want to print a paper copy of the slides before each class for cross-reference during class, for study, and for taking notes on. The slides are available from Blackboard or my teaching page on the WEB: I also invite you to visit my home page and research page: Some more recent papers can be found at

Textbook There is no formal textbook.

Teaching AssistanceWe will be assisted by two second-year MSF students, Shuo Liu ( 314-397-0625) and Kun Xue ( 314-269-6816).

Of course, you can also direct your questions to me; I recommend e-mail at or a text to 314-398-3196 as an effective way of tracking me down quickly.

About you In addition to enrolling through the proper authorities, please send me an e-mail with the following information:

If you enroll and later choose to drop the class, please let me know about that, too, with feedback about why the course didn't work for you.

About me I was previously a tenured full professor at Yale, and I came to Wash U in 1988 in the hope of building a top finance group, which we have done. More information on me is in the chatty blurb at or in my vitae at All of my Web pages can be accessed through my home page.

Feedback Feedback is especially important to me. Written feedback by e-mail is especially useful.

Integrity Students are expected to conform to the Olin School's Code of Conduct. Any violations will be reported with sadness and a strong sense of duty.

Summary I invite you to join me in exploring the exciting applications of optimization to finance!