Nonlinear Systems Estimation: Asset Pricing Model Application

  • Stephen J. Brown


In this chapter we consider the application of Mathematica in the context of estimating a simultaneous system of nonlinear equations. The particular application involves the estimation of asset pricing models. This subject is a staple of the financial economics literature. The objective is not to show how Mathematica can be used to solve problems of this type. Indeed, the program is not well suited to this kind of large scale numerical optimization. Rather, the intent is to show how Mathematica can be used in conjunction with more specialized software products for this purpose.


Risk Premium Capital Asset Price Model Asset Price Model Spelling Error Arbitrage Price Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Black, Fischer, Michael Jensen, and Myron Scholes, 1972. “The Capital Asset Pricing Model: Some Empirical Tests,” in Jensen, Michael C. (ed.) Studies in the Theory of Capital Markets, New York: Praeger.Google Scholar
  2. Brown, Stephen and Toshiyuki Otsuki, 1992. “Risk Premia in Pacific Rim Capital Markets,” (Unpublished working paper, Department of Finance, Stern School, NYU.)Google Scholar
  3. Brown, Stephen and Mark Weinstein, 1983. “A New Approach to Testing Asset Pricing Models: The Bilinear Paradigm,” Journal of Finance 38, 711–743.CrossRefGoogle Scholar
  4. Chen, N-F., R. Roll, and S. Ross, 1986. “Economic Forces and the Stock Market,” Journal of Business 59, 383–404.CrossRefGoogle Scholar
  5. Connor, Gregory and Robert Korajczyk, 1988. “Risk and Return in an Equilibrium APT: Application of a New Test Methodology,” Journal of Financial Economics, 21, 255–290.CrossRefGoogle Scholar
  6. Fama, Eugene and James MacBeth, 1973. “Risk, Return and Equilibrium: Empirical Tests,” Journal of Political Economy 81, 607–636.CrossRefGoogle Scholar
  7. Ferson, Wayne, 1990. “Are the Latent Variables in Time-varying Expected Returns Compensation for Consumption Risk?” Journal of Finance 45, 397–430.CrossRefGoogle Scholar
  8. Goldfeld, S., and Richard Quandt, 1972. Nonlinear Methods in Econometrics, Amsterdam: North Holland.zbMATHGoogle Scholar
  9. Greene, William, 1990. Econometric Analysis, New York: Macmillan Publishing Company.Google Scholar
  10. Hansen, Lars and Kenneth Singleton, 1982. “Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models,” Econometrica 50,1269–1286.MathSciNetCrossRefzbMATHGoogle Scholar
  11. Luenberger, D. G, 1984. Linear and Nonlinear Programming, Reading, MA: AddisonWesley.zbMATHGoogle Scholar
  12. McElroy, Margery and Edwin Burmeister, 1988. “Arbitrage Pricing Theory as a Restricted Nonlinear Regression Model,” Journal of Business and Economic Statistics 6, 29–42.Google Scholar
  13. Richard Roll and Stephen Ross, 1980. “An Empirical Investigation of the Arbitrage Pricing Theory,” Journal of Finance 35, 1073–1102.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Stephen J. Brown

There are no affiliations available

Personalised recommendations