University of Michigan
School of Business Administration

Course Syllabus
Finance 872


Tyler Shumway
Office: D6207
Phone: 763-4129
Home Page: http:\\\~shumway

Course Objective:

Finance 872 is an introduction to continuous-time asset pricing. It is designed primarily for second-year Ph.D. students in finance, but it may also be of interest to financial engineering students, economics students, or very motivated MBA students. In F872 we discuss continuous-time stochastic processes, and then we apply techniques for manipulating those processes to several classic finance problems. Among other things, we derive Merton's intertemporal CAPM, the Black-Scholes formula, and the Cox-Ingersoll-Ross term structure model.

F872 is much more mathematically rigorous than the typical MBA course, but it is probably less rigorous than most economics Ph.D. courses. It uses many mathematical statistics concepts, some fundamental finance ideas, and a little bit of dynamic programming. If your financial/statistical background is weak I strongly recommend that you take BA855 before F872.

Course Material:

Course materials will include a number of academic papers, chapters from several different textbooks, and some course notes. Useful reference books include:

Duffie, Darrell, 1992, Dynamic asset pricing theory, Princeton University Press, Princeton, New Jersey.

Huang, Chi-fu, and Robert H. Litzenberger, 1988, Foundations for Financial Economics, North-Holland, New York.

Ingersoll, Jonathan E., 1987, Theory of Financial Decision Making, Rowman & Littlefield, Savage, Maryland.

Merton, Robert C., 1994, Continuous-Time Finance, Blackwell, Cambridge, Massachusetts.

Shimko, David C., 1992, Finance in Continuous Time: A Primer, Kolb, Miami, Florida.


There will be both a final exam and weekly homework assignments to complete. The final exam will count for 75% of your grade and the homework assignments will count for the remaining 25%. The final will probably be a timed take-home exam. We will discuss the answers to homework problems in class. You should come prepared to discuss your answers each week.

Course Outline:

The course outline is not a weekly schedule. Some of the topics will take more than one session to cover and other topics will take less time. Most topics are accompanied by reading assignments listed below.

  1. Continuous time
  2. Shimko, chapter 1

  3. Utility maximization in continuous time
  4. Ingersoll, chapter 13

  5. Option pricing
  6. Fisher Black and Myron Scholes, 1973, "The Pricing of Options and Corporate Liabilities," Journal of Political Economy 81, 637-654.

  7. Option Pricing with Stochastic Volatility
  8. Steven L. Heston, 1993, "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies 6, 327-343.

  9. No arbitrage in continuous time
  10. Duffie, chapter 6

  11. Pricing other securities - term structure models
  12. Duffie, chapter 7

  13. Models for pricing risky debt
  14. Darrell Duffie and Kenneth J. Singleton, 1999, "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies 12, 687-720.