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Affine General Equilibrium Models

  • Bjørn Eraker

    ()

    (Department of Economics, Duke University, Durham, North Carolina 27708)

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    No-arbitrage models are extremely flexible modelling tools but often lack economic motivation. This paper describes an equilibrium consumption-based CAPM framework based on Epstein-Zin preferences, which produces analytic pricing formulas for stocks and bonds under the assumption that macro growth rates follow affine processes. This allows the construction of equilibrium pricing formulas while maintaining the same flexibility of state dynamics as in no-arbitrage models. In demonstrating the approach, the paper presents a model that incorporates inflation such that asset prices are nominal. The model takes advantage of the possibility of non-Gaussian shocks and model macroeconomic uncertainty as a jump-diffusion process. This leads to endogenous stock market crashes as stock prices drop to reflect a higher expected rate of return in response to sudden increases in risk. The nominal yield curve in this model has a positive slope if expected inflation growth negatively impacts real growth. This model also produces asset prices that are consistent with observed data, including a substantial equity premium at moderate levels of risk aversion.

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    File URL: http://dx.doi.org/10.1287/mnsc.1070.0796
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 54 (2008)
    Issue (Month): 12 (December)
    Pages: 2068-2080

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    Handle: RePEc:inm:ormnsc:v:54:y:2008:i:12:p:2068-2080
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    7. Fatih Guvenen, 2005. "A Parsimonious Macroeconomic Model for Asset Pricing: Habit Formation of Cross-sectional Heterogeneity?," Finance 0507009, EconWPA.
    8. Monika Piazzesi & Martin Schneider, 2006. "Equilibrium Yield Curves," NBER Working Papers 12609, National Bureau of Economic Research, Inc.
      • Monika Piazzesi & Martin Schneider, 2007. "Equilibrium Yield Curves," NBER Chapters, in: NBER Macroeconomics Annual 2006, Volume 21, pages 389-472 National Bureau of Economic Research, Inc.
    9. John Y. Campbell & Robert J. Shiller, 1986. "Cointegration and Tests of Present Value Models," Cowles Foundation Discussion Papers 785, Cowles Foundation for Research in Economics, Yale University.
    10. John Y. Campbell, 1992. "Intertemporal Asset Pricing Without Consumption Data," NBER Working Papers 3989, National Bureau of Economic Research, Inc.
    11. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    12. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    13. Duffee, Gregory R., 2006. "Term structure estimation without using latent factors," Journal of Financial Economics, Elsevier, vol. 79(3), pages 507-536, March.
    14. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    15. J. B. Taylor & M. Woodford (ed.), 1999. "Handbook of Macroeconomics," Handbook of Macroeconomics, Elsevier, edition 1, volume 1, number 1.
    16. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    17. C. Gourieroux & A. Monfort & V. Polimenis, 2006. "Affine Models for Credit Risk Analysis," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(3), pages 494-530.
    18. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    19. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, 08.
    20. Campbell, J.Y. & Shiller, R.J., 1988. "Stock Prices, Earnings And Expected Dividends," Papers 334, Princeton, Department of Economics - Econometric Research Program.
    21. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    22. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, 06.
    23. Philippe Weil, 1989. "The Equity Premium Puzzle and the Riskfree Rate Puzzle," NBER Working Papers 2829, National Bureau of Economic Research, Inc.
    24. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
    25. Andrew Ang & Monika Piazzesi, 2001. "A No-Arbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables," NBER Working Papers 8363, National Bureau of Economic Research, Inc.
    26. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-69, July.
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