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Latent Variable Models for Stochastic Discount Factors

  • GARCIA, René
  • RENAULT, Éric

Latent variable models in finance originate both from asset pricing theory and time series analysis. These two strands of literature appeal to two different concepts of latent structures, which are both useful to reduce the dimension of a statistical model specified for a multivariate time series of asset prices. In the CAPM or APT beta pricing models, the dimension reduction is cross-sectional in nature, while in time-series state-space models, dimension is reduced longitudinally by assuming conditional independence between consecutive returns, given a small number of state variables. In this paper, we use the concept of Stochastic Discount Factor (SDF) or pricing kernel as a unifying principle to integrate these two concepts of latent variables. Beta pricing relations amount to characterize the factors as a basis of a vectorial space for the SDF. The coefficients of the SDF with respect to the factors are specified as deterministic functions of some state variables which summarize their dynamics. In beta pricing models, it is often said that only the factorial risk is compensated since the remaining idiosyncratic risk is diversifiable. Implicitly, this argument can be interpreted as a conditional cross-sectional factor structure, that is, a conditional independence between contemporaneous returns of a large number of assets, given a small number of factors, like in standard Factor Analysis. We provide this unifying analysis in the context of conditional equilibrium beta pricing as well as asset pricing with stochastic volatility, stochastic interest rates and other state variables. We address the general issue of econometric specifications of dynamic asset pricing models, which cover the modern literature on conditionally heteroskedastic factor models as well as equilibrium-based asset pricing models with an intertemporal specification of preferences and market fundamentals. We interpret various instantaneous causality relationships between state variables and market fundamentals as leverage effects and discuss their central role relative to the validity of standard CAPM-like stock pricing and preference-free option pricing.

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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2000-01.

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Length: 31 pages
Date of creation: 2000
Date of revision:
Handle: RePEc:mtl:montde:2000-01
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  1. Gary Chamberlain & Michael Rothschild, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," NBER Working Papers 0996, National Bureau of Economic Research, Inc.
  2. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
  3. Hansen, Lars Peter & Richard, Scott F, 1987. "The Role of Conditioning Information in Deducing Testable," Econometrica, Econometric Society, vol. 55(3), pages 587-613, May.
  4. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  5. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
  6. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  7. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-.
  9. Francis X. Diebold & Marc Nerlove, 1986. "The dynamics of exchange rate volatility: a multivariate latent factor ARCH model," Special Studies Papers 205, Board of Governors of the Federal Reserve System (U.S.).
  10. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  11. Florens, J P & Mouchart, M, 1982. "A Note on Noncausality," Econometrica, Econometric Society, vol. 50(3), pages 583-91, May.
  12. MEDDAHI, Nour & RENAULT, Éric, 1998. "Aggregations and Marginalization of GARCH and Stochastic Volatility Models," Cahiers de recherche 9818, Universite de Montreal, Departement de sciences economiques.
  13. Harvey, Campbell R, 1991. " The World Price of Covariance Risk," Journal of Finance, American Finance Association, vol. 46(1), pages 111-57, March.
  14. Jan Kallsen & Murad S. Taqqu, 1998. "Option Pricing in ARCH-type Models," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 13-26.
  15. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  16. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
  17. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  18. 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.
  19. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  20. Garcia, R. & Luger, R. & Renault, E., 2001. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Cahiers de recherche 2001-09, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  21. Turnbull, Stuart M & Milne, Frank, 1991. "A Simple Approach to Interest-Rate Option Pricing," Review of Financial Studies, Society for Financial Studies, vol. 4(1), pages 87-120.
  22. Gabriele Fiorentini & Enrique Sentana Iváñez, 1997. "Conditional means of time series processes and time series processes for conditional means," Working Papers. Serie AD 1997-17, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  23. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1981. "A Re-examination of Traditional Hypotheses about the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 36(4), pages 769-99, September.
  24. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237.
  25. Amin, Kaushik I & Ng, Victor K, 1993. " Option Valuation with Systematic Stochastic Volatility," Journal of Finance, American Finance Association, vol. 48(3), pages 881-910, July.
  26. King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-33, July.
  27. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  28. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  29. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-52, September.
  30. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
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