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

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  • Xavier Gabaix

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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Bibliographic Info

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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Citations

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Cited by:
  1. Xavier Gabaix, 2012. "Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance," The Quarterly Journal of Economics, Oxford University Press, vol. 127(2), pages 645-700.
  2. Kristensen, Dennis & Mele, Antonio, 2011. "Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models," Journal of Financial Economics, Elsevier, Elsevier, vol. 102(2), pages 390-415.
  3. Dimitri Vayanos & Jean-Luc Vila, 2009. "A preferred-habitat model of the term structure of interest rates," LSE Research Online Documents on Economics 29308, London School of Economics and Political Science, LSE Library.
  4. Hanno Lustig & Stijn Van Nieuwerburg & Adrien Verdelhan, 2007. "The Wealth-Consumption Ratio: A Litmus Test for Consumption-based Asset Pricing Models¤," Boston University - Department of Economics - Working Papers Series, Boston University - Department of Economics WP2007-030, Boston University - Department of Economics.
  5. Christian Julliard & Anisha Ghosh, 2008. "Can rare events explain the equity premium puzzle?," LSE Research Online Documents on Economics 4808, London School of Economics and Political Science, LSE Library.
  6. Yu Chen & Thomas Cosimano & Alex Himonas, 2010. "Continuous time one-dimensional asset-pricing models with analytic price–dividend functions," Economic Theory, Springer, Springer, vol. 42(3), pages 461-503, March.
  7. François Gourio, 2008. "Time-series predictability in the disaster model," Boston University - Department of Economics - Working Papers Series, Boston University - Department of Economics wp2008-016, Boston University - Department of Economics.
  8. JULES H. van BINSBERGEN & RALPH S. J. KOIJEN, 2010. "Predictive Regressions: A Present-Value Approach," Journal of Finance, American Finance Association, American Finance Association, vol. 65(4), pages 1439-1471, 08.
  9. Sang Byung Seo & Jessica A. Wachter, 2013. "Option Prices in a Model with Stochastic Disaster Risk," NBER Working Papers 19611, National Bureau of Economic Research, Inc.
  10. John H. Cochrane, 2014. "A Mean-Variance Benchmark for Intertemporal Portfolio Theory," Journal of Finance, American Finance Association, American Finance Association, vol. 69(1), pages 1-49, 02.
  11. Igor Halperin & Andrey Itkin, 2013. "USLV: Unspanned Stochastic Local Volatility Model," Papers 1301.4442, arXiv.org, revised Mar 2013.
  12. Emmanuel Farhi, 2008. "Rare Disasters and Exchange Rates," 2008 Meeting Papers 47, Society for Economic Dynamics.
  13. Roger Farmer, 2014. "Asset Prices in a Lifecycle Economy," NBER Working Papers 19958, National Bureau of Economic Research, Inc.

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