Course: Continous - Time Finance Semester: Fall 1995



Continuous-Time Finance Semester: Fall 2001

Course Number: FINA 323

Professor: Isabelle Bajeux-Besnainou, Ph.D.

Class time: Monday – 12:30 – 3:00 PM – Lisner 430

Office hours: Mondays- Wednesdays – 10:00 AM–12:00 PM or by appointment.

Office: Room #2 – Finance department - 2101 F St, NW.

Tel: 202-994-2559

Fax: 202-994-5014

E-mail: bajeux@gwu.edu.

Course Description: Lectures and article presentations in continuous-time finance.

Readings: Mandatory readings will be indicated in class. Extensive lecture notes are distributed in class. No book purchase is mandatory.

Course Objective: Modern Financial Theory has become more and more technical with the development of continuous-time models. While being a relatively new field, Continuous-Time Finance becomes more recognized since the Nobel prize in Economics have been awarded to Robert Merton and Myron Scholes for their work on pricing models of derivative securities.

After a review of the mathematical background needed for these models, we will go over the most important continuous-time models in class. This will include pricing of derivative securities, consumption-portfolio selection models, continuous-time CAPM, CCAPM, APT and yield curve models.

Method of grading:

Mid-term exam: 60%

Paper and presentation: 40%

Prometheus:

All students need to register with Prometheus to get timely information about various course events during the semester. To do so, go to the web site and create a new student account (unless you already have one). You will have to enter your name, email, a username and a password for creating this new account. Once you have created your account, you can access the web-site of this course using:

Course ID : 36659

Password : FINA323

Please note that you should create this account ASAP otherwise you might miss some important announcements which will be listed on our course web-site.

References (books):

(DO) Dothan, M., Prices in Financial Markets, Oxford University Press, 1990.

(D) Duffie, D., Dynamic Asset Pricing Theory, Princeton University Press, 1992.

(CP) Cossin Didier and Hugues Pirotte, Advanced Credit Risk Analysis, Wiley, 2001.

(HL) Huang, C.F., and R. Litzenberger, 1988, Foundations for Financial Economics, Amsterdam: North-Holland.

(H) Hull, J., Options, Futures, and Other Derivative Securities. Englewood Cliffs, NJ,

Prentice Hall, 2000, 4th edition.

(K) Karatzas Ioannis and Steven Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag, 1988.

(MB) Malliaris, A. and W. Brock, Stochastic Methods in Economics and Finance, North Holland, 1982.

(M1) Merton, R. Continuous - Time Finance, Basil Blackwell, 1990.

(MR) Musiela, Marek and Marek Rutkowski. Martingale Methods in Financial Modelling, Springer, 1998.

(N) Neftci, S. An Introduction to the Mathematics of Financial Derivatives, 1996, Academic Press.

(S) Shimko, D., Finance in Continuous Time, Kolb Publishing Company, 1992.

(WHD) Wilmott, P.,Howison S. and J. Dewynne, 1997, The Mathematics of Financial Derivatives, Cambridge University Press.

References (articles):

(BP1) Bajeux, I. and R. Portait, “ The Numeraire Portfolio: A new Approach to Financial Theory”, The European Journal of Finance, 1997.

(BP2) Bajeux, I. and R. Portait, “Dynamic Asset Allocation in a Mean-Variance model”, Management Science, 1998.

(BP3) Bajeux, I., Jordan J. and R. Portait, 2001, September, American Economic Review, “The Stock/Bond ratio asset allocation puzzle: comment.”

(B) Black, F., “The Pricing of Commodity Contracts”, Journal of Financial Economics, 3, 1976, 167-179.

(BS) Black, F. and M. Scholes, “The Pricing of Options and Corporate Liabilities”

Journal of Political Economy, 81, 1973 pp. 637-654.

(BrS) Brennan, M. and E. Schwartz, 1979, “ A Continuous Time Approach to the Pricing of Bonds”, Journal of Banking and Finance 3, 133-155.

(CH) Cox, J., and C-F. Huang, “Optimal Consumption and Portfolio Policies When Asset Prices Follow a Diffusion Process” Journal of Economic Theory, 49, pp. 33-83. 1989.

(CIR1) Cox, J., J. Ingersoll, and S. Ross, “A Theory of the Term Structure of Interest Rates,” Econometrica 53, pp. 385-408, 1985.

(CIR2) Cox, J., J. Ingersoll and S. Ross, “An Intertemporal General Equilibrium Model of Asset Prices,” Econometrica 53, pp. 363-384, 1985.

(CRR) Cox, J, S. Ross and M. Rubinstein (1979), “Option Pricing: A Simplified Approach,” Journal of Financial Economics 7, September, pp. 229-263.

(HP) Harrison, J.M. and S. Pliska, “Martingales and Stochastic Integrals in the Theory of Continuous Trading,” Stochastic Processes and their Applications, 11, pp. 215-260

(HJM1) Heath, D., R. Jarrow, and A. Morton, “Bond Pricing and the Term Structure of Interest Rates: A New Methodology” Econometrica 1988

(HJM2) Heath, D., R. Jarrow, and A. Morton, “Bond Pricing and the Term Structure of Interest Rates: A Discrete-Time Approximation” Journal of Financial and Quantitative Analysis 1990

(KLS) Karatzas, I., J. Lehoczky, and S. Shreve, “Optimal Portfolio and Consumption Decisions for a “Small Investor” on a Finite Horizon” SIAM Journal of Control and Optimization 25, pp. 1157-86, 1987.

(L) Litzenberger, R., “Prices of State-Contingent Claims implicit in Option Prices”, Journal of Business, 1978, vol. 51, no. 4.

(M2) Merton, R. “Optimal Consumption and Portfolio Rules in a Continuous - Time Model,” Journal of Economic Theory 3, 1971, pp. 373-413.

(M3) Merton, R. “An Intertemporal Capital Asset Pricing Model,” Econometrica, 41, pp. 867-888.

(M4) Merton, R. “The Theory of Rational Option Pricing”,(1973), Bell Journal of Economics and Management Science, 4, 141-183.

(V) Varian, “The Arbitrage Principle in Financial Economics” Journal of Economic Perspectives, vol. 1, no 2, pp. 55-72.

(Va) Vasicek, O. “An Equilibrium Characterization of the Term Structure” Journal of Financial Economics 5 : 177-88

Class Schedule

Session 1- 2

Stochastic processes- handout to be distributed. Random variables- filtration - tribes

brownian motions- stochastic processes

Martingales - stochastic integrals.

Itô lemma.

Readings: Handout; (S), (N), (WHD).

Assignment: Short problems-Applications.

Session 3-4

Arbitrage principle. Application to option pricing in the binomial model.

Readings: (CRR), (V), (L), (SC).

Session 5

Risk-neutral probabilities. A discrete-time example.

Readings: Handout.

Session 6-7

Valuation of derivative securities. The Black/Scholes model.

Yield curve models

Readings: (H), (BS),(M4), (SM), (B).

Readings: (D), (Va), (BrS), (HJM1), (HJM2), (CIR1), (CIR2).

Session 8-9

Intertemporal consumption- portfolio selection models. Dynamic Asset Allocations models. The Numeraire Portfolio - Intertemporal CAPM, CCAPM, APT.

Readings: (D), (M), (M3), (BP), (M2), (D), (KLS), (CH).

Session 10

Mid-term exam

Sessions 11-12-13-14

Students presentation of final paper.

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