Skip to main content

Diffusion Models of Asset Prices

  • Chapter
  • First Online:
Handbook of Computational Finance

Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

  • 5674 Accesses

Abstract

This paper reviews the literature on asset pricing in diffusion models. The first part is devoted to equilibrium models based on the representative agent paradigm. Explicit formulas for fundamental equilibrium quantities such as the state price density, the interest rate and the market price of risk are presented. Valuation formulas for stocks and contingent claims are also provided. Numerical implementation of the model is carried out in a setting with constant relative risk aversion. The second part of the paper focuses on multiagent models with complete financial markets. Characterizations of equilibrium are reviewed and numerical algorithms for computation are proposed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Back, K. (1991). Asset pricing for general processes. Journal of Mathematical Economics, 20, 371–395.

    Article  MathSciNet  MATH  Google Scholar 

  • Berrada, T. (2006). Incomplete information, heterogeneity and asset pricing. Journal of Financial Econometrics, 4, 136–160.

    Article  Google Scholar 

  • Breeden, D. (1979). An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of Financial Economics, 7, 265–296.

    Article  MATH  Google Scholar 

  • Breeden, D. (1986). Consumption, production, inflation and interest rates: A synthesis. Journal of Financial Economics, 16, 3–39.

    Article  Google Scholar 

  • Cox, J. C., & Huang, Cf. (1989). Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory, 49, 33–83.

    Article  MathSciNet  MATH  Google Scholar 

  • Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985). An intertemporal general equilibrium model of asset prices. Econometrica, 53, 363–384.

    Article  MathSciNet  MATH  Google Scholar 

  • Detemple, J., & Serrat, A. (2003). Dynamic equilibrium with liquidity constraints. Review of Financial Studies, 16, 597–629.

    Article  Google Scholar 

  • Detemple, J., Garcia, R., & Rindisbacher, M. (2008). Simulation methods for optimal portfolios. In J. R. Birge & V. Linetsky (Eds.), Handbooks in operations research and management science, Financial engineering (Vol. 15, pp. 867–923). Amsterdam: Elsevier.

    Google Scholar 

  • Detemple, J. B., & Zapatero, F. (1991). Asset prices in an exchange economy with habit formation. Econometrica, 59, 1633–1657.

    Article  MATH  Google Scholar 

  • Detemple, J. B., Garcia, R., & Rindisbacher, M. (2003). A Monte-Carlo method for optimal portfolios. Journal of Finance, 58, 401–446.

    Article  Google Scholar 

  • Duffie, D., & Zame, W. (1989). The consumption-based capital asset pricing model. Econometrica, 57, 1279–1297.

    Article  MathSciNet  MATH  Google Scholar 

  • Dumas, B. (1989). Two-person dynamic equilibrium in the capital market. Review of Financial Studies, 2, 157–188.

    Article  Google Scholar 

  • Gallmeyer, M., & Hollifield, B. (2008). An examination of heterogeneous beliefs with a short-sale constraint in a dynamic economy. Review of Finance, 12, 323–364.

    Article  MATH  Google Scholar 

  • Grossman, S. J., & Shiller, R. J. (1981). The determinants of the variability of stock market prices. American Economic Review, 71, 222–227.

    Google Scholar 

  • Grossman, S. J., Melino, A., & Shiller, R. J. (1987). Estimating the continuous-time consumption-based asset-pricing model. Journal of Business and Economic Statistics, 5, 315–328.

    Google Scholar 

  • Hansen, L. P., & Singleton, K. J. (1983). Stochastic consumption, risk aversion, and the temporal behavior of asset returns. Journal of Political Economy, 91, 249–268.

    Article  Google Scholar 

  • Huang, Cf. (1987). An intertemporal general equilibrium asset pricing model: The case of diffusion information. Econometrica, 55, 117–142.

    Article  MathSciNet  MATH  Google Scholar 

  • Karatzas, I., & Shreve, S. E. (1998). Methods of mathematical finance. Berlin: Springer.

    MATH  Google Scholar 

  • Karatzas, I., Lehoczky, J. P., & Shreve, S. E. (1987). Optimal portfolio and consumption decisions for a “small investor” on a finite horizon. SIAM Journal of Control and Optimization, 25, 1557–1586.

    Article  MathSciNet  MATH  Google Scholar 

  • Karatzas, I., Lehoczky, J. P., & Shreve, S. E. (1990). Existence, uniqueness of multi-agent equilibrium in a stochastic, dynamic consumption/investment model. Mathematics of Operations Research, 15, 80–128.

    Article  MathSciNet  MATH  Google Scholar 

  • Karatzas, I., Lakner, P., Lehoczky, J. P., & Shreve, S. E. (1991). Dynamic equilibrium in a simplified stochastic economy with heterogeneous agents. In Stochastic analysis: liber amicorum for Moshe Zakai (pp. 245–272). New York: Academic.

    Google Scholar 

  • Kloeden, P. E., & Platen, E. (1999). Numerical solution of stochastic differential equations (3rd ed.). Berlin: Springer.

    Google Scholar 

  • Mehra, R., & Prescott, E. C. (1985). The equity premium: A puzzle. Journal of Monetary Economics, 15, 145–61.

    Article  Google Scholar 

  • Merton, R. C. (1971). Optimum consumption and portfolio rules in a continuous time model. Journal of Economic Theory, 3, 373–413.

    Article  MathSciNet  Google Scholar 

  • Merton, R. C. (1973). An intertemporal capital asset pricing model. Econometrica, 41, 867–87.

    Article  MathSciNet  MATH  Google Scholar 

  • Ocone, D., & Karatzas, I. (1991). A generalized Clark representation formula, with application to optimal portfolios. Stochastics and Stochastics Reports, 34, 187–220.

    MathSciNet  MATH  Google Scholar 

  • Pliska, S. (1986). A stochastic calculus model of continuous trading: Optimal portfolios. Mathematics of Operations Research, 11, 371–382.

    Article  MathSciNet  Google Scholar 

  • Wang, J. (1996). The term structure of interest rates in a pure exchange economy with heterogeneous investors. Journal of Financial Economics, 41, 75–110.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jérôme Detemple .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Detemple, J., Rindisbacher, M. (2012). Diffusion Models of Asset Prices. In: Duan, JC., Härdle, W., Gentle, J. (eds) Handbook of Computational Finance. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17254-0_3

Download citation

Publish with us

Policies and ethics