Finance 9100, Fall, 2001 The Theory of Asset Valuation

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1 Finance 9100, Fall, 2001 The Theory of Asset Valuation Instructor Professor David C. Nachman Office: CBA 1239 Phone: Office Hours: M 5:00-7:00 P. M., or by appointment Prerequisites Consent of Instructor. You should know at least elementary calculus, linear algebra, and probability and statistics. If you do not know how to calculate an expectation or variance or covariance you had better see me immediately. Course Objective and Content This course will acquaint students with the modern theory of asset valuation. The focus of the course is the study of asset pricing under uncertainty from the perspective of the three basic constraints on asset prices: the absence of arbitrage, single investor optimality, and market equilibrium. Topics include state prices, discount factors, the fundamental theorem of asset pricing, spanning, market completeness, market prices of risk, the term structure of interest rates, and the pricing of derivative securities in both continuous-time and discrete-time. Course Material Required text material: (C) John H. Cochrane, 2001, Asset Pricing, Princeton University Press, Princeton, New Jersey. (D) Darrell Duffie, 2001, Dynamic Asset Pricing Theory, 3 nd ed., Princeton University Press, Princeton, New Jersey. (H) John C. Hull, 2000, Options, Futures, & Other Derivatives, 4 th ed. Prentice Hall, Upper Saddle River, New Jersey. (LW) Stephen F. LeRoy and Jan Werner, 2001, Principles of Financial Economics, Cambridge University Press, Cambridge, UK.

2 (N) David C. Nachmsn, 1999, Notes on Hilbert Space, handout. Some notes and papers may be handed out throughout the semester as the need arises. There are several good Ph.D. level texts that can serve as references for this course. These are mentioned at the end of this syllabus with some brief comments. Course Work and Grades A topic outline with reading assignments follows. Reading assignments are in (C), (D), (LW), and (N). There is one reading assignment from (H). Lectures will be from (C). There will be four or five graded homework assignments (HW), classroom presentations (CP), and a final exam (FE). (HW) assignments consist of three or four exercises at the end of relevant chapters in (C) and (D) and will be announced in class. No late homework will be graded. You can use any reference material that you like in doing the homework, but you must give complete and explicit references. The work that you hand in must be your own work and it must demonstrate that you know what to do and how to do it. (CP) Students will be assigned text material from (C) to present in class. The assignments will be made in class. Look at the topic outline for these assignments. If it is possible, your choice (first, second, third?) will be your assignment. (FE) The final exam (FE) is Monday, December 10, 2001, 7:15 PM, as per the official final exam schedule. A student's grade will be determined from a weighted average of grades on the homework assignments, class presentations, and the final exam using the following weighting scheme: 10% for each (HW), 30% for (CP), and 30% for (FE). Topic Outline and Reading/Question/Problem/Case Assignments* Class Day/Date Topic/Assignments 1 M 8/20 Introduction to payoff spaces, (N), (D) Appendices A and C. Consumption Based Model and Overview, (C) Chapter 1, (D) Chapter 1, (LW) Chapter 1. 2 M 8/27 Applying the Basic Model, (C) Chapter 2. Contingent Claims Markets, (C)

3 Chapter 3. 3 M 9/3 Labor Day 4 M 9/10 The Discount Factor, (C) Chapter 4. (D) Appendix B. (LW) Chapters 2, 3, 5, 6. 5 M 9/17 Mean-Variance Frontier and Beta Representations, (C) Chapter 5. (LW) Chapter M 9/24 Relation between Discount Factors, Betas, and Mean-Variance Frontiers, (C) Chapter 6. (LW) Chapters 15, M 10/1 Implications of Existence and Equivalence Theorems, (C) Chapter 7. Conditioning Information, (C) Chapter 8. (D) Chapter 2. 8 M 10/8 Factor Pricing Models, (CP), (C) Chapter 9, Introduction and Section M 10/15 Factor Pricing Models, (CP), (C) Chapter 9, Section 9.2 and M 10/22 Factor Pricing Models, (CP), (C) Chapter 9, Section 9.4 and M 10/29 Option Pricing, (CP), (C) Chapter 17. (D) Chapter M 11/5 Option Pricing without Perfect Replication, (CP), (C) Chapter 18, Section 18.1 and Section M 11/12 Option Pricing without Perfect Replication, (CP), (C) Chapter 18, Section 18.3 and Section M 11/19 Term Structure of Interest Rates, (CP), (C) Chapter 19, Sections 19.1,19.2, and M 11/26 Term Structure of Interest Rates, (CP), (C) Chapter 19, Section 19.4, (H) Chapter M 12/3 Term Structure of Interest Rates, (CP), (C) Chapter 19, Section * This topic/assignment outline provides a general plan for the course. Changes may be necessary. If such changes are necessary, they will be announced in class and students will be responsible for accommodating them. Below are some references, organized roughly by subject, that may be useful for this course. Some brief comments follow the list.

4 ASSET PRICING: Campbell, John, Andrew Lo, and A. Craig MacKinlay, 1997,The Econometrics of Financial Markets, Princeton University Press, Princeton, New Jersey. Cochrane, John H., 2001, Asset Pricing, Princeton University Press, Princeton, New Jersey. Duffie, Darrell, 1988, Security Markets: Stochastic Models, Academic Press, Boston. Duffie, Darrell, 2001, Dynamic Asset Pricing Theory, 3 rd Princeton, New Jersey. ed., Princeton University Press, 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. LeRoy, Stephen F., and Jan Werner, 2001, Principles of Financial Economics, Cambridge University Press, Cambridge, UK. Merton, Robert C., 1994, Continuous-Time Finance, Blackwell, Cambridge, Massachusetts. Milne, Frank, 1995, Finance Theory and Asset Pricing, Clarendon Press, Oxford. ECONOMICS: Kreps, David M., 1990, A Course in Microeconomic Theory, Princeton University Press, Princeton, New Jersey. Magill, Michael, and Martine Quinzii, 1996, Theory of Incomplete Markets: Volume 1, MIT Press, Cambridge, Massachusetts. Mas-Colell, Andreu, Michael D. Whinston, and Jerry R. Green, 1995, Microeconomic Theory, Oxford University Press, New York. Simon, Carl P., and Lawrence Blume, 1994, Mathematics for Economists, W. W. Norton & Company, New York. Varian, Hal. R., 1992, Microeconomic Analysis, third edition, W. W. Norton & Company, New York.

5 DERIVATIVE PRICING AND MATHEMATICAL FINANCE: Baxter, Martin, and Andrew Rennie, 1996, Financial Calculus: An Introduction to Derivative Pricing, Cambridge University Press, Cambridge. Bingham, N. H., and Rüdiger Kiesel, Risk-Neutral Valuation, Springer-Verlag, New York. Björk, Tomas, 1998, Arbitrage Theory in Continuous Time, Oxford University Press, New York. Elliott, Robert J., and P. Ekkehard Kopp, 1999, Mathematics of Financial Markets, Springer- Verlag, New York. Fouque, Jean-Pierre, George Papanicolaou, and K. Ronnie Sircar, 2000, Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, Cambridge, UK. Hull, John C., 2000, Options, Futures, & Other Derivatives, Prentice Hall, Upper Saddle River, New Jersey. Hunt, P. J., and J. E. Kennedy, 2000, Financial Derivatives in Theory and Practice, John Wiley & Sons, LTD, New York. Kallianpur, Gopinath, and Rajeeva L. Karandikar, 2000, Introduction to Option Pricing Theory, Birkhauser, Boston. Karatzas, Ioannis, 1997, Lectures on the Mathematics of Finance, American Mathematical Society, Providence, Rhode Island. Karatzas, Ioannis, and Steven E. Shreve, 1998, Methods of Mathematical Finance, Springer- Verlag, New York. Korn, Ralf, and Elke Korn, 2000, Option Pricing and Portfolio Optimization: Modern Methods of Financial Mathematics, Graduate Studies in Mathematics Volume 31, American Mathematical Society, Providence, Rhode Island. Kwok, Y. K., 1998, Mathematical Models of Financial Derivatives, Springer-Verlag, Singapore. Lamberton, Damien, and Bernard Lapeyre, 1996, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall, London. Meyer, Michael, 2001, Continuous Stochastic Calculus with Applications to Finance, Chapman & Hall/CRC, New York. Mikosch, Thomas, 1999, Elementary Stochastic Calculus with Finance in View, World Scientific Publishing Co. Pte. Ltd., Singapore. Musiela, Marek, and Marek Rutkowski, 1997, Martingale Methods in Financial Modelling, Springer-Verlag, Berlin. Neftci, Salih N., 1996, An Introduction to the Mathematics of Financial Derivatives, Academic Press, San Diego.

6 Nielsen, Lars Tyge, 1999, Pricing and Hedging of Derivative Securities, Oxford University Press, New York. Shaw, William, 1999, Modeling Financial Derivatives with Mathematica, Cambridge University Press, Cambridge, UK. Shimko, David C., 1992, Finance in Continuous Time: Primer, Kolb, Miami, Florida. Shiryaev, Albert N., 1999, Essentials of Stochastic Finance: Facts, Models, Theory, World Scientific Publishing Co. Pte. Ltd., Singapore. Steele, J. Michael, 2001, Stochastic Calculus and Financial Applications, Springer, New York. PROBABILITY AND STOCHASTIC PROCESSES: Arnold, Ludwig, 1973, Stochastic Differential Equations: Theory and Applications, John Wiley & Sons, New York. Breiman, Leo, 1968, Probability, Addison-Wesley Publishing, Reading, Massachusetts. Jacod, Jean, and Philip Protter, 1999, Probability Essentials, Springer-Verlag, New York. Karatzas, Ioannis, and Steven E. Shreve, 1988, Brownian Motion and Stochastic Calculus, Springer-Verlag, New York. Karlin, Samuel, and Howard M. Taylor, 1975, A First Course in Stochastic Processes, 2 nd ed., Academic Press, New York. Karlin, Samuel, and Howard M. Taylor, 1981, A Second Course in Stochastic Processes, Academic Press, New York. Neveu, J., 1975, Discrete Parameter Martingales, North-Holland Publishing Co., Amsterdam. Øksendal, Bernt, 1998, Stochastic Differential Equations, 5 th ed., Springer-Verlag, Berlin. Resnick, Sidney I., 2001, A Probability Path, Birkhauser, Boston. Rogers, L. C. G., and D. Williams, 1994, Diffusions, Markov Processes, and Martingales, Volume 1: Foundations, 2 nd ed., John Wiley & Sons, New York. Rogers, L. C. G., and D. Williams, 1987, Diffusions, Markov Processes, and Martingales, Volume 2: Itô Calculus, John Wiley & Sons, New York. Williams, David, 1991, Probability with Martingales, Cambridge University Press, Cambridge. You ought to seriously consider purchasing several of the books in the category ASSET PRICING. It will be difficult to have a satisfying graduate school experience and a good academic/research career without understanding the material in most of them. Of course you must get the books for this course. You do not have to buy the Hull book. It was not ordered for this course. I will hand out copies of the relevant chapter assigned. However, it is an excellent book that no serious finance academic should be without. So buy it.

7 If you are only going to purchase one book other than the books for this course, I suggest that you buy Campbell, Lo, and MacKinlay. It treats empirical issues as well as theory and it is reasonably up-to-date and comprehensive (from the perspective of their own work). In the category ECONOMICS, the books by Varian and Simon and Blume will be referenced frequently in this course. You need a good microeconomics text and a good reference for the basic mathematics used in economics. These are the best I know of. The book by Magill and Quinzii is an excellent reference on the economic theory of incomplete asset market economies. As you can see from the above list, the literature on derivatives and financial mathematics has exploded. The Baxter and Rennie and the Neftci books in this category are true introductions. The book by Nielsen presents the mathematics of derivative pricing in a more complete and digestible form than any other source above while not getting bogged down in a lot of rigor. For me, I find the books by Lamberton and Lapeyre, Meyer, and Steele, to be excellent references although they may be advanced. The Jacod and Protter text and the Resnick text provide the easiest introduction to the probability theory that underlies the theory of stochastic processes. You should realize, however, that this material is not easy at all, and the theory of stochastic processes, say at the level of Karatsas and Shreve (1988), is a long way off from this introduction. The book by Williams (1991) also provides such an introduction and is a good introduction to discrete parameter martingales with a hint at finance applications. The book by Neveu is a treasure in this literature.

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