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Nonlinear Properties of Multifactor Financial Models

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Author Info
Chen, Kim Heng
Jandhyala, Venkata K.
Fotopoulos, Stergios B.
Abstract

This paper provides a comprehensive analysis of the nonlinear properties of multifactor pricing models. Beginning with the generalized geometric Brownian motion, we develop a method whereby the log returns of a set of d-assets or portfolios admit a scale mixture model. This is followed by an analytical study on the conditional behavior of a subset of assets given another subset. Expressions for the first two conditional moments are provided under the scale mixture family. The regression equation when the scaling variable is constant (unity) corresponds with the renowned APT. Computable conditional moment expressions for the scaling variable are derived under both inverse gamma and gamma distributions. These moment equations are nonlinear in parameters, apart from containing the usual linear terms under the APT. We then apply the above nonlinear methodology to the log asset returns of four major companies in the U.S. stock market.

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Article provided by Review of Applied Economics in its journal Review of Applied Economics.

Volume (Year): 1 (2005)
Issue (Month): 2 ()
Pages:
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Handle: RePEc:ags:reapec:49157

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Related research
Keywords: Generalized Geometric Brownian Motion; Heteroskedasticity; Scale Mixture of Normal Distributions; Research Methods/ Statistical Methods; C31; C44; G12;

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  1. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September. [Downloadable!] (restricted)
  2. Ferson, Wayne E & Korajczyk, Robert A, 1995. "Do Arbitrage Pricing Models Explain the Predictability of Stock Returns?," Journal of Business, University of Chicago Press, vol. 68(3), pages 309-49, July. [Downloadable!] (restricted)
  3. Bansal, Ravi & Viswanathan, S, 1993. " No Arbitrage and Arbitrage Pricing: A New Approach," Journal of Finance, American Finance Association, vol. 48(4), pages 1231-62, September. [Downloadable!] (restricted)
  4. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265. [Downloadable!] (restricted)
  5. Connor, Gregory & Korajczyk, Robert A., 1988. "Risk and return in an equilibrium APT : Application of a new test methodology," Journal of Financial Economics, Elsevier, vol. 21(2), pages 255-289, September. [Downloadable!] (restricted)
  6. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January. [Downloadable!] (restricted)
  7. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September. [Downloadable!] (restricted)
    Other versions:
  8. Jobson, John D, 1982. " A Multivariate Linear Regression Test for the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 37(4), pages 1037-42, September. [Downloadable!] (restricted)
  9. Dhrymes, Phoebus J & Friend, Irwin & Gultekin, N Bulent, 1984. " A Critical Reexamination of the Empirical Evidence on the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 39(2), pages 323-46, June. [Downloadable!] (restricted)
  10. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59. [Downloadable!] (restricted)
  11. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," Journal of Business, University of Chicago Press, vol. 47(2), pages 244-80, April. [Downloadable!] (restricted)
  12. Gerhard, Frank & Hautsch, Nikolaus, 2002. "Volatility estimation on the basis of price intensities," Journal of Empirical Finance, Elsevier, vol. 9(1), pages 57-89, January. [Downloadable!] (restricted)
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  13. Milne, Frank, 1988. "Arbitrage and Diversification in a General Equilibrium Asset Economy," Econometrica, Econometric Society, vol. 56(4), pages 815-40, July. [Downloadable!] (restricted)
  14. Frank Milne & Dilip Madan, 1991. "Option Pricing With V. G. Martingale Components," Working Papers 1159, Queen's University, Department of Economics. [Downloadable!]
  15. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," Journal of Business, University of Chicago Press, vol. 63(4), pages 511-24, October. [Downloadable!] (restricted)
  16. Fama, Eugene F, 1991. " Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-617, December. [Downloadable!] (restricted)
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