1 University of Washington at Seattle School of Business and Administration Asset Pricing - FIN 592 Office: MKZ 267 Phone: (206) 543 1843 Fax: (206) 221 6856 E-mail: jduarte@u.washington.edu http://faculty.washington.edu/jduarte/ Lectures: Mondays and Wednesdays: 1:30-3:20pm BLM: 415 1. Course Description One part of this course is an introduction to theoretical continuous time non-arbitrage theory, while the other part covers some methodologies used in empirical asset pricing literature. Emphasis is given to the fixed income literature. The topics covered are: 1) Ito s lemma. Brownian motion. Markov processes. PDE s. F-K. 2) No-arbitrage. Black and Scholes-Merton model. The equivalence between non-arbitrage and the existence of an equivalent martingale measure. 3) The non-parametric estimation of the SPD. 4) Mathematical tools used to price derivatives: Monte Carlo Simulation, Partial Differential Equations, and Binomial Trees. 5) Term structure models. Estimation of continuous time term-structure models. Term structure derivatives. The course is intended for Ph.D. students interested in asset pricing. This course is very quantitative and requires basic familiarity with a variety of mathematical concepts, such as partial differential equations. 2. Course Objectives After completing this course you should be able to: 1) Use the general non-arbitrage framework to price derivatives. 2) Apply continuous time techniques to models in Finance. 3) Use econometric techniques such as Monte Carlo simulation, GMM, kernel regression, maximum likelihood. 4) Describe the current issues in the term structure and in the derivatives literature 3. Prerequisites Students must be comfortable with calculus and statistics. Many homework assignments will require the use of some statistical package. You may use any statistical package you wish. For those of you that intend to do serious research in this field, I recommend Gauss or Matlab. The course is very demanding. 4. Course Requirements The course requirements consist of problem sets and a take home final exam.
2 5. Problem Sets Problem sets contain questions and computer exercises meant to help you practice on you own. The problem sets are individual. You may discuss the homework questions with your colleagues however you are required to turn in your individual homework. A penalty of 10% of the problem set grade will be applied to late problem sets. I expect you to read all the required reading material. If you do not have time to read all the required readings then you should consider sharing paper summaries with your colleagues. I will ask questions about the papers in the exam and in the problem sets. 6. Questions and Office Hours You can ask questions by e-mail (jduarte@u.washington.edu). I welcome your feedback on every aspect of the course. If you would prefer to be anonymous drop a note in my MKZ 268 mailbox. Send me e-mails with questions any time you wish. If you think that you will need extended help, please e-mail me to make an appointment. I encourage you to participate in the class. Don t be shy about asking questions to clarify what we are discussing. Every lecture and the course as a whole builds on what we learned previously, so being lost gets very costly very quickly. At the other extreme, a good sign that you are asking too many questions is when the rest of the class starts noticing and the value of the class gets reduced for the other student. 7. Exams and Grading The final will be graded from 0 to 40 points. Your course grade is: (0.5 * final grade + 0.5 * problem sets grade) /10 The final exam is a take home exam. The questions for this exam will be given to you in the last class of the course (Wednesday, March 12 th ). The final exam is strictly individual. You must turn in your answers directly to me until Wednesday, March 19 th at 5:00pm. If you cannot find me, you may leave your answers below the door of my office (MKZ 267). The re-grading policy for the exam or problem set is: 1) If you think that a question in your exam or problem set was graded incorrectly, then write a very precise description of your concern and give it to me with your exam. 2) I will re-grade your entire exam (problem set). There is no guarantee that the grade initially assigned will not be lowered. 3) Re-grading will only be considered within seven days of your receiving your grade back. 8. Class Attendance and Administrative Notes Class attendance is not mandatory. I expect you to arrive on time for the class but if you arrive late, please do so in way that does not disturb the class. You may get class handouts in my web page. 9. Academic Accommodations To request academic accommodations due to disability, please contact disabled Student Services, 448 Schmitz, (206) 543-8914 (V/TTY). If you have a letter from Disabled Student Services indicating that you
3 have a disability that requires academic accommodations, please present the letter to me so we can discuss the accommodations you might need in this class. 10. Texts The following material is highly recommended in this course: Campbell, Lo, and MacKinley, 1996, The Econometrics of Financial Markets (An excellent book for all asset pricing students) Duffie D., 2001, Dynamic Asset Pricing Theory 3 rd edition (A book that all Ph.D. students interested in continuous time finance should have) Hull, J., 2002, Options, Futures and Other Derivatives, 5 th edition (A book that anyone interested in derivatives should have.) Duffie D. and Singleton K., 2003, Credit Risk: Pricing, Measurement, and Management, 1 st edition (a very recent book in a topic that has been receiving a lot of attention) Gourieroux and Jasiak, 2001, Financial Econometrics: Problems, Models, and Methods (An interesting book in financial econometrics) Campbell and Viceira, 2002, Strategic Asset Allocation, Portfolio Choice for Long Term Investors. ( A good survey of a classic financial problem) Reference books for researchers in empirical Finance Hamilton, Time Series Analysis Greene, Econometric Analysis 11. Course Outline and Readings The readings marked with the sign are required. 0) SAS by Lewis Thorson 1) Tools Probability Space Definitions, Indicator Functions, Expectations, LIE; Filtration, Stochastic process, Adapted process, Martingale, Brownian Motion; Markov process, Diffusion, SDE, Ito s Lemma, Feynman-Kac, Fokker-Planck PDE, conditional density. Duffie Appendix C to E Hamilton, 8.1, 8.3 14.1-14.2, 5.1-5.2 2) Market Efficiency. Consumption-based models and the equity premium puzzle. Fama. E., 1991, Efficient Capital Markets II, JF, vol XLVI, no5. Constantinides, G., 2002, Rational Asset Pricing, JF, vol LVII, no.4 Campbell et. al., 1996 p. 304 to p. 314.
4 Campbell and Cochrane, The Journal of Political Economy, Vol. 107, No. 2. (Apr., 1999), pp. 205-251. Hansen and Singleton, 1982, Generalized Instrumental Variables Estimation of Nonlinear Rational Expectation Models, Econometrica, vol. 50, #5. Hansen and Singleton, 1983, Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns, JPE, 91 issue 2 p. 249-265. Brav, Constantinides, Geczy, 2002 Asset Pricing with Heterogeneous Consumers and Limited Participation: Empirical Evidence, JPE, vol. 110, no. 4 Aït-Sahalia, Parker and Yogo, 2003, Luxury Goods and the Equity Premium, Princeton University WP., download at http://www.princeton.edu/~yacine/richc.pdf 3) A First Attack into the Black and Scholes formula Continuous time derivation of the formula Limitations of the Model and Extensions Estimating Volatility Parameter Merton, R. C., spring 1973, Theory of Rational Option Pricing, pp. 141-183, Bell Journal of Economics and Management Science, 4. Merton, 1976, Option Pricing When the Underlying Stock Returns are Discontinuous, JFE. Campbell et. al. chapter 9 Duffie chapter 5 Nelson, D.B., 1990, ARCH models as diffusions approximations, Journal of Econometrics, 45 4) Risk Neutral Probability Measure or Equivalent Martingale Measure A generalized method of derivative pricing The Risk Neutral Density Implications for Binomial Trees Nonparametric Estimation of the Risk Neutral Density Aït-Sahalia and Duarte, 2003, Nonparametric Option Pricing under Shape Restrictions, forthcoming in the Journal of Econometrics Breeden and Litzenberger, 1978, Prices of State-Contingent Claims Implicit in Option Prices, Journal of Business Wand and Jones, 1995, Kernel Smoothing, Chapman & Hall, London. Duffie chapter 6
5 5) Numerical Methods Trees Discretization of PDE s Methods based on F-K Duffie chapter 12 from A to H 6) One Factor Term Structure Models Vasicek and CIR models Non-parametric estimation of the short-term interest rate Monte Carlo simulation as a tool to test estimators Duffie chapter 7 from A to G Campbell et. al., chapter 10 Vasicek, O., August 1977, An Equilibrium Characterization of the Term Structure, pp. 177-188, Journal of Financial Economics, 5, North-Holland Publishing Company. Cox, J.C., Ingersoll, J.E. and Ross, S. A., March 1985, A Theory of the Term Structure of Interest Rates, pp. 385-407, Econometrica, vol. 53. Aït-Sahalia, Testing Continuous-Time Models of the Spot Interest Rate, 1996, RFS, 9, 385-426 Pritsker, 1998, RFS, 11, 3, 449-487 7) Multifactor models PCA Multifactor affine models Generalization of the CIR model, Vasicek, general affine models; Quadratic Term Structure Models; Tests of Affine Term Structure Models; Objective of HJM; Duffie chapter 7 from H to K Duffie, D. and Kan, R., 1996, A Yield Factor Model of Interest Rates. Mathematical Finance, vol. 6 no. 4, 379-406. Ahn, Dittmar and Gallant, 2002, Quadratic Term Structure Models: theory and evidence, RFS, 15, p. 243. Litterman, R. and Scheinkman, J., June 1991, Common Factors Affecting Bond Returns, pp. 54-61, Journal of Fixed Income. Duffie, D. and Singleton, K., 1997, An Econometric Model of the Term Structure of Interest- Rate Swap Yield, The Journal of Finance, vol. 52, pp. 1287-1321. Dai, Q. and Singleton, K., 2000, Specification Analysis of Affine Term Structure Models, The Journal of Finance, vol. 55, pp. 1943-1978.
6 Dai, Q. and Singleton, K.J., 2002, Expectation Puzzles, Time-varying Risk Premia, and Dynamic Models of the Term Structure. Journal of Financial Economics 63, 415-441. Dai, Q. and Singleton, K.J., 2003, Term Structure Dynamics in Theory and Reality, forthcoming Review of Financial Studies. Duarte, J., 2001, Evaluating Alternative Risk Preferences in Affine Term Structure Models, University of Washington in Seattle Working Paper. 8) Some Interest Rate Derivatives: Swaptions and Caps Puzzle Longstaff, Santa-Clara and Schwartz, 2001, The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence Driessen, Klaassen and Melemberg, 2002, The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions, forthcoming in the JFQA 9) Corporate Securities Merton. R. C., May 1974, On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, The Journal of Finance, vol. 29, pp. 449-470. Duffie Chapter 11