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Linearity-Generating Processes: A Modelling Tool Yielding Closed Forms for Asset Prices

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Author Info
Xavier Gabaix

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Abstract

This methodological paper presents a class of stochastic processes with appealing properties for theoretical or empirical work in finance and macroeconomics, the "linearity-generating" class. Its key property is that it yields simple exact closed-form expressions for stocks and bonds, with an arbitrary number of factors. It operates in discrete and continuous time. It has a number of economic modeling applications. These include macroeconomic situations with changing trend growth rates, or stochastic probability of disaster, asset pricing with stochastic risk premia or stochastic dividend growth rates, and yield curve analysis that allows flexibility and transparency. Many research questions may be addressed more simply and in closed form by using the linearity-generating class.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 13430.

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Date of creation: Sep 2007
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Handle: RePEc:nbr:nberwo:13430

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Find related papers by JEL classification:
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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References listed on IDEAS
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.:
  1. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, MIT Press, vol. 121(2), pages 461-504, May. [Downloadable!] (restricted)
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  2. Mariano M. Croce & Martin Lettau & Sydney C. Ludvigson, 2007. "Investor Information, Long-Run Risk, and the Duration of Risky Cash-Flows," NBER Working Papers 12912, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02. [Downloadable!] (restricted)
  4. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 20(1), pages 1-39, January. [Downloadable!] (restricted)
  5. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," Journal of Business, University of Chicago Press, vol. 51(3), pages 453-75, July. [Downloadable!] (restricted)
  6. Antonio Mele, 2003. "Fundamental Properties of Bond Prices in Models of the Short-Term Rate," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 16(3), pages 679-716, July. [Downloadable!] (restricted)
    Other versions:
  7. Xavier Gabaix & David Laibson, 2002. "The 6D Bias and the Equity Premium Puzzle," Harvard Institute of Economic Research Working Papers 1947, Harvard - Institute of Economic Research. [Downloadable!]
  8. Lubos PÁstor & Veronesi Pietro, 2003. "Stock Valuation and Learning about Profitability," Journal of Finance, American Finance Association, vol. 58(5), pages 1749-1790, October. [Downloadable!] (restricted)
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  9. Mele, Antonio, 2007. "Asymmetric stock market volatility and the cyclical behavior of expected returns," Journal of Financial Economics, Elsevier, vol. 86(2), pages 446-478, November. [Downloadable!] (restricted)
  10. Emmanuel Farhi & Xavier Gabaix, 2008. "Rare Disasters and Exchange Rates," NBER Working Papers 13805, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  11. Campbell, John Y & Shiller, Robert J, 1991. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," Review of Economic Studies, Blackwell Publishing, vol. 58(3), pages 495-514, May. [Downloadable!] (restricted)
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  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. Lars Peter Hansen & John Heaton & Nan Li, 2005. "Consumption Strikes Back?: Measuring Long-Run Risk," NBER Working Papers 11476, National Bureau of Economic Research, Inc.
  14. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April. [Downloadable!] (restricted)
  15. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 1(3), pages 195-228. [Downloadable!] (restricted)
    Other versions:
  16. Tano Santos & Pietro Veronesi, 2006. "Labor Income and Predictable Stock Returns," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 19(1), pages 1-44. [Downloadable!] (restricted)
  17. Lars Peter Hansen & Jose Scheinkman, 2006. "Long Term Risk: An Operator Approach," NBER Working Papers 12650, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  18. Timothy C. Johnson, 2002. "Rational Momentum Effects," Journal of Finance, American Finance Association, vol. 57(2), pages 585-608, 04. [Downloadable!] (restricted)
  19. Harry Mamaysky, 2002. "A Model For Pricing Stocks and Bonds," Yale School of Management Working Papers ysm279, Yale School of Management. [Downloadable!]
  20. Fama, Eugene F & French, Kenneth R, 1996. " Multifactor Explanations of Asset Pricing Anomalies," Journal of Finance, American Finance Association, vol. 51(1), pages 55-84, March. [Downloadable!] (restricted)
  21. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 15(1), pages 243-288, March.
  22. Lubos Pástor & Pietro Veronesi, 2005. "Rational IPO Waves," Journal of Finance, American Finance Association, vol. 60(4), pages 1713-1757, 08. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, 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.)

  1. Emmanuel Farhi & Xavier Gabaix, 2008. "Rare Disasters and Exchange Rates," NBER Working Papers 13805, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  2. Xavier Gabaix, 2008. "Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance," NBER Working Papers 13724, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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This page was last updated on 2008-11-16.

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