Dynamic Asset Pricing Theory

Dynamic Asset Pricing Theory:

Tentative Syllabus

October15,2005

I Course Description

This course introduces PhD students to advanced techniques for modeling asset prices in a continuous-time setting.This encompasses no-arbitrage characterization of asset prices; no-arbitrage pricing of derivative securities;dynamic portfolio and consumption choice un-der uncertainty;and equilibrium characterization of asset prices.Equipped with techniques (such as applications of Ito’s lemma,Girsanov’s theorem,and Feynman-Kac theorem,dy-namic programming and martingale methods,etc),students are invited to develop a deeper understanding of some important asset pricing models in the continuous-time framework, both by reading the original papers and by working through problem sets designed to en-hance the students’understanding of those models and to illustrate the application of the continuous-time methods.

II Topics covered

1.WEEK1:Review of Dynamic Programming:Du?e(1996),Sargent(1987)

?With and without uncertainty

?Discrete-time and Continuous-time

2.WEEK2:Arbitrage and Martingales:Du?e(1996),chapter6,Harrison and

Kreps(1979),Dybvig and Huang(1989),Back and Pliska(1991)*1

3.WEEK3:Complete Markets:Hedging and Pricing Contingent Claims:

Du?e(1996),Chapters5and8,Black and Scholes(1973),Merton(1973b)*,Karatzas (1988)*,Du?e and Stanton(1992)*

4.WEEK4:Complete Markets:Optimal Consumption and Portfolio Choice:

Du?e(1996),Chapter9,Merton(1971),Cox and Huang(1989),Cox and Huang (1991)*,Karatzas,Lehoszky,and Shreve(1987)*

5.WEEK5:Dynamic Equilibrium with Complete Markets:Du?e(1996),

Chapter A-H,J,Merton(1973a)*,Breeden(1979)*,Karatzas,Lehoszky,and Shreve (1990),Lucas(1978),survey:Cochrane(1999)

1An asterisk denotes that material can be skipped on a?rst reading.

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6.WEEK6:Models of the Term Structure:Du?e(1996),Chapter7and Chapter

10,Section I,Cox,Ingersoll,and Ross(1985a),Cox,Ingersoll,and Ross(1985b), Heath,Jarrow,and Morton(1992),survey:Dai and Singleton(2001)

7.WEEK7:Incomplete markets:He and Pearson(1991),Telmer(1993),Karatzas,

Lehoszky,Shreve,and Xu(1991)*

8.WEEK8:Issues in modern asset pricing

?Session I:Beyond the Standard Framework

–Recursive Utility:Epstein and Zin(1989),Du?e and Epstein(1992)

–Robustness Preference:Anderson,Hansen,and Sargent(2000)

–Learning:Brennan and Xia(1998)

–Disappointment aversion:Gul(1991),Ang,Bekaert,and Liu(2005)

–Myopic loss aversion:Kahneman and Tversky(1979),Benartzi and Thaler (1995)

–Habit Persistence:Sundaresan(1989),Constantinides(1990),Campbell and Cochrane(1999),Detemple and Zapatero(1991)*

?Session II:Asset pricing puzzles and conditional empirical regularities:Mehra

and Prescott(1985),Weil(1989),Campbell(1999),Fama(1984),Fama and Bliss

(1987),Campbell and Shiller(1991),Fama and French(1989),Dai and Singleton

(2002)

III Course Materials

Required reading

?Lecture notes

?Du?e(1996)

?Original papers

Supplemental reading

?Sargent(1987),Merton(1992),Ingersoll(1987),Cochrane(2001)

IV Problem Sets and Exams

Grades will be based on the following:

?Problem Sets(70%)

?Final Exam(30%,open book)

You are encouraged to discuss among yourselves on the course material.However,you must attack and submit your homework and?nal problems individually.

If you get stuck with some problems in your homework or?nal,you can get hints from me for a price:a reduction in the grades proportional to the amounts of hints received.

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References

Anderson,E.W.,Hansen,L.P.,Sargent,T.J.,2000.Robustness,detection and the price of risk.Working paper,University of North Carolina,University of Chicago,and Stanford University.

Ang,A.,Bekaert,G.,Liu,J.,2005.Why stocks may disappoint.forthcoming,Journal of Financial Economics.

Back,K.,Pliska,S.,1991.On the fundamental theorem of asset pricing with an in?nite state space.Journal of Mathematical Economics20,1–18.

Benartzi,S.,Thaler,R.H.,1995.Myopic loss aversion and the equity premium puzzle.

Quarterly Journal of Economics pp.73–92.

Black,F.,Scholes,M.,1973.The pricing of options and corporate liabilities.Journal of Political Economy81,637–654.

Breeden,D.,1979.An intertemporal asset pricing model with stochastic consumption and investment opportunities.Journal of Financial Economics7,265–296.

Brennan,M.J.,Xia,Y.,1998.Stock price volatility,learning,and the equity premium.

Working paper,Anderson School of Management,UCLA.

Campbell,J.,Cochrane,J.,1999.By force of habit:A consumption-based explanation of aggregate stock market behavior.Journal of Political Economy107(2),205–251.

Campbell,J.Y.,1999.Handbook of MacroeconomicsNorth-Holland,Amsterdam vol.1 chap.Asset Prices,Consumption,and the Business Cycle,chapter19.

Campbell,J.Y.,Shiller,R.J.,1991.Yield spreads and interest rate movements:A bird’s eye view.Review of Economic Studies58,495–514.

Cochrane,J.H.,1999.New facts in?nance.Economic Perspectives XXIII.

,2001.Asset Pricing.Princeton University Press,Princeton,NJ,.

Constantinides,G.,1990.Habit formation:A resolution of the equity premium puzzle.

Journal of Political Economy98(3),519–543.

Cox,J.C.,Huang,C.F.,1989.Optimal consumption and portfolio choices when asset prices follows a di?usion process.Journal of Economic Theory49,33–83.

,1991.A variational problem arising in?nancial economics.Journal of Mathematical Economics20,465–487.

Cox,J.C.,Ingersoll,J.E.,Ross,S.A.,1985a.An intertemporal general equilibrium model of asset prices.Econometrica53,363–384.

,1985b.A theory of the term structure of interest rates.Econometrica53,385–408.

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Dai,Q.,Singleton,K.,2001.Handbook of the Economics and FinanceElsevier Science Pub Co chap.Fixed Income Pricing.

Dai,Q.,Singleton,K.J.,2002.Expectations puzzles,time-varying risk premia,and a?ne models of the term structure.Journal of Financial Economics63.

Detemple,J.B.,Zapatero,F.,1991.Asset prices in an exchange economy with habit for-mation.Econometrica59(6),1633–1657.

Du?e,D.,1996.Dynamic Asset Pricing Theory.Princeton University Press,2nd edition,.

Du?e,J.D.,Epstein,L.,1992.Stochastic di?erential utility.Econometrica60(2),353–394.

Du?e,J.D.,Stanton,R.,1992.Pricing continuously resettled contingent claims.Journal of Economic Dynamics16,561–573.

Dybvig,P.H.,Huang,C.F.,1989.Nonnegative wealth,absence of arbitrage,and feasible consumption plans.Review of Financial Studies1,377–401.

Epstein,L.,Zin,S.,1989.Substitution,risk aversion and the temporal behavior of con-sumption and asset returns i:A theoretical framework.Econometrica57,937–969.

Fama,E.,1984.Term premiums in bond returns.Journal of Financial Economics13,529–546.

Fama,E.,Bliss,R.,1987.The information in long-maturity forward rates.American Eco-nomic Review77(4),680–692.

Fama,E.,French,K.,1989.Business conditions and expected returns on stocks and bonds.

Journal of Financial Economics25,23–49.

Gul,F.,1991.A theory of disappointment aversion.Econometrica59(3),667–686.

Harrison,M.,Kreps,D.,1979.Martingales and arbitrage in multiperiod securities markets.

Journal of Economic Theory20,381–408.

He,H.,Pearson,N.,1991.Consumption and portfolio choices with incomplete markets and short-sale constraints:The in?nite-dimensional case.Journal of Economic Theory54, 259–305.

Heath,D.,Jarrow,R.,Morton,A.,1992.Bond pricing and the term structure of interest rates:A new methodology.Econometrica60,77–105.

Ingersoll,J.,1987.Theory of Financial Decision Making.Rowman and Little?eld,.

Kahneman,D.,Tversky,A.,1979.Prospect theory:An analysis of decision under risk.

Econometrica47,263–291.

Karatzas,I.,1988.On the pricing of american options.Applied Mathematics and Optimiza-tion17,37–60.

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Karatzas,I.,Lehoszky,J.P.,Shreve,S.E.,1987.Optimal protfolio and consumption deci-sions for a“small investor”on a?nite hoziron.SIAM Journal on Control and Optimiza-tion25,1557–1586.

,1990.Existence and uniqueness of multi-agent equilibrium in a stochastic,dynamic consumption/investment model.Mathematics of Operations Research15,80–128.

Karatzas,I.,Lehoszky,J.P.,Shreve,S.E.,Xu,G.L.,1991.Martingale and duality meth-ods for utility maximization in an incomplete market.SIAM Journal on Control and Optimization29,702–730.

Lucas,R.,1978.Asset prices in an exchange economy.Econometrica46,1429–1445.

Mehra,R.,Prescott,E.C.,1985.The equity premium:A puzzle.Journal of Monetary Economics15,145–161.

Merton,R.C.,1971.Optimum consumption and portfolio rules in a continuous time model.

Journal of Economic Theory3,373–413.

,1973a.An intertemporal capital asset pricing model.Econometrica41(5),867–887.

,1973b.Theory of rational option pricing.Bell Journal of Economics and Manage-ment Science4,141–183.

,1992.Continuous-time Finance.Blackwell,Cambridge,MA,&Oxford,UK,.

Sargent,T.J.,1987.Dynamic macroeconomic Theory.Harvard University Press,Cam-bridge,MA and London,England,.

Sundaresan,S.M.,1989.Intertemporally dependent preferences and the volatility of con-sumption and wealth.Review of Financial Studies2,73–88.

Telmer,C.,1993.Asset-pricing puzzles and incomplete markets.Journal of Finance48, 1803–1832.

Weil,P.,1989.The equity premium puzzle and the riskfree rate puzzle.Journal of Monetary Economics24,401–421.

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