Analytic solving of asset pricing models: The by force of habit case
Analytic methods for solving asset pricing models are developed to solve asset pricing models. Campbell and Cochrane's [1999. By force of habit, a consumption-based explanation of aggregate stock market behavior. Journal of Political Economy 107, 205-251] habit persistence model provides a prototypical example to illustrate this method. When the parameters involved satisfy certain conditions, the integral equation of this model has a solution in the space of continuous functions that grows exponentially at infinity. However, the parameters advocated by Campbell and Cochrane do not satisfy one of these conditions. The existence problem is removed by restricting the price-dividend function to avoid values of dividend growth that are extreme. Thus, existence and uniqueness of the solution in the space of continuous and bounded functions is proved. Using complex analysis the price-dividend function is also shown to be analytic in a region large enough to cover all relevant values of dividend growth. Next, a numerical method is presented for computing higher order polynomial approximations of the solution. Finally, a uniform upper bound on the error of these approximations is derived. An intensive search of the parameter space results in no parameter values for which the solution matches the historic equity premium and Sharpe ratio within Campbell and Cochrane's model.
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- Santos, Manuel S., 1999. "Numerical solution of dynamic economic models," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 5, pages 311-386 Elsevier.
- Epstein, Larry G. & Zin, Stanley E., 1990.
"'First-order' risk aversion and the equity premium puzzle,"
Journal of Monetary Economics,
Elsevier, vol. 26(3), pages 387-407, December.
- L. Epstein & S. Zin, 2010. "First order risk aversion and the equity premium puzzle," Levine's Working Paper Archive 1400, David K. Levine.
- Geweke, John, 2001. "A note on some limitations of CRRA utility," Economics Letters, Elsevier, vol. 71(3), pages 341-345, June.
- Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-82, September.
- John Y. Campbell & John H. Cochrane, 1995.
"By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior,"
NBER Working Papers
4995, National Bureau of Economic Research, Inc.
- John Y. Campbell & John H. Cochrane, 1994. "By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," CRSP working papers 412, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
- Cochrane, John H. & Campbell, John, 1999. "By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Scholarly Articles 3119444, Harvard University Department of Economics.
- John Y. Campbell & John H. Cochrane, 1994. "By force of habit: a consumption-based explanation of aggregate stock market behavior," Working Papers 94-17, Federal Reserve Bank of Philadelphia.
- Barro, Robert, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," Scholarly Articles 3208215, Harvard University Department of Economics.
- Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
- Charles Engel & Kenneth D. West, 2003.
"Exchange rates and fundamentals,"
Federal Reserve Bank of San Francisco, issue Mar.
- Choi, Horag & Mark, Nelson C. & Sul, Donggyu, 2008.
"Endogenous discounting, the world saving glut and the U.S. current account,"
Journal of International Economics,
Elsevier, vol. 75(1), pages 30-53, May.
- Horag Choi & Nelson C. Mark & Donggyu Sul, 2007. "Endogenous Discounting, the World Saving Glut and the U.S. Current Account," NBER Working Papers 13571, National Bureau of Economic Research, Inc.
- Yu Chen & Thomas Cosimano & Alex Himonas, 2008. "Solving an asset pricing model with hybrid internal and external habits, and autocorrelated Gaussian shocks," Annals of Finance, Springer, vol. 4(3), pages 305-344, July.
- Abel, A.B., 1990.
"Asset Prices Under Habit Formation And Catching Up With The Joneses,"
Weiss Center Working Papers
1-90, Wharton School - Weiss Center for International Financial Research.
- Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
- A. Abel, 2010. "Asset prices under habit formation and catching up with the Jones," Levine's Working Paper Archive 1395, David K. Levine.
- Andrew B. Abel, . "Asset Prices Under Habit Formation and Catching Up With the Jones," Rodney L. White Center for Financial Research Working Papers 01-90, Wharton School Rodney L. White Center for Financial Research.
- Andrew B. Abel, . "Asset Prices Under Habit Formation and Catching Up With the Jones," Rodney L. White Center for Financial Research Working Papers 1-90, Wharton School Rodney L. White Center for Financial Research.
- Andrew B. Abel, 1990. "Asset Prices under Habit Formation and Catching up with the Joneses," NBER Working Papers 3279, National Bureau of Economic Research, Inc.
- Ovidiu L. Calin & Yu Chen & Thomas F. Cosimano & Alex A. Himonas, 2005. "Solving Asset Pricing Models when the Price-Dividend Function Is Analytic," Econometrica, Econometric Society, vol. 73(3), pages 961-982, 05.
- Rajnish Mehra & Edward C. Prescott, 2003.
"The Equity Premium in Retrospect,"
NBER Working Papers
9525, National Bureau of Economic Research, Inc.
- Blume, Lawrence & Easley, David & O'Hara, Maureen, 1982. "Characterization of optimal plans for stochastic dynamic programs," Journal of Economic Theory, Elsevier, vol. 28(2), pages 221-234, December.
- Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
- Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
- Wachter, Jessica A., 2006. "A consumption-based model of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 79(2), pages 365-399, February.
- Santos, Manuel S, 1993. "On High-Order Differentiability of the Policy Function," Economic Theory, Springer, vol. 3(3), pages 565-70, July.
- R. Mehra & E. Prescott, 2010.
"The equity premium: a puzzle,"
Levine's Working Paper Archive
1401, David K. Levine.
- Philippe Weil, 1989.
"The Equity Premium Puzzle and the Riskfree Rate Puzzle,"
NBER Working Papers
2829, National Bureau of Economic Research, Inc.
- Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
- Phillippe Weil, 1997. "The Equity Premium Puzzle and the Risk-Free Rate Puzzle," Levine's Working Paper Archive 1833, David K. Levine.
- Samuelson, Paul A, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances, and Higher Moments," Review of Economic Studies, Wiley Blackwell, vol. 37(4), pages 537-42, October.
- Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
- Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-86, April.
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