Nonlinear Properties of Multifactor Financial Models
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Review of Applied Economics in its journal Review of Applied Economics.
Volume (Year): 1 (2005)
Issue (Month): 2 ()
Contact details of provider:
Web page: http://www.lincoln.ac.nz/story11874.html
Generalized Geometric Brownian Motion; Heteroskedasticity; Scale Mixture of Normal Distributions; Research Methods/ Statistical Methods; C31; C44; G12;
Find related papers by JEL classification:
- C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
- C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Milne, Frank, 1988. "Arbitrage and Diversification in a General Equilibrium Asset Economy," Econometrica, Econometric Society, vol. 56(4), pages 815-40, July.
- 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.
- 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.
- Frank Milne & Dilip Madan, 1991.
"Option Pricing With V. G. Martingale Components,"
1159, Queen's University, Department of Economics.
- Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
- Ferson, Wayne E & Korajczyk, Robert A, 1995. "Do Arbitrage Pricing Models Explain the Predictability of Stock Returns?," The Journal of Business, University of Chicago Press, vol. 68(3), pages 309-49, July.
- Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-80, April.
- Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
- Gary Chamberlain & Michael Rothschild, 1984.
"Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets,"
NBER Working Papers
0996, National Bureau of Economic Research, Inc.
- 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.
- Chamberlain, Gary & Rothschild, Michael, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Scholarly Articles 3230355, Harvard University Department of Economics.
- 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.
- Cambanis, Stamatis & Fotopoulos, Stergios B. & He, Lijian, 2000. "On the Conditional Variance for Scale Mixtures of Normal Distributions," Journal of Multivariate Analysis, Elsevier, vol. 74(2), pages 163-192, August.
- Frank Gerhard & Nikolaus Hautsch, 1999.
"Volatility Estimation on the Basis of Price Intensities,"
CoFE Discussion Paper
99-19, Center of Finance and Econometrics, University of Konstanz.
- 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.
- Stergios Fotopoulos & Lijian He, 1999. "Error Bounds for Asymptotic Expansion of the Conditional Variance of the Scale Mixtures of the Multivariate Normal Distribution," Annals of the Institute of Statistical Mathematics, Springer, vol. 51(4), pages 731-747, December.
- 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.
- Fama, Eugene F, 1991. " Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-617, December.
- Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September.
- 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.
- Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-24, October.
- Tina Hviid Rydberg, 1999. "Generalized Hyperbolic Diffusion Processes with Applications in Finance," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 183-201.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (AgEcon Search).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.