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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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Cited by:
  1. Hanno Lustig, . "The Wealth-Consumption Ratio: A Litmus Test for Consumption-based Asset Pricing Models," UCLA Economics Online Papers 420, UCLA Department of Economics.
  2. Jean-Luc Vila & Dimitri Vayanos, 2009. "A Preferred-Habitat Model of the Term Structure of Interest Rates," FMG Discussion Papers dp641, Financial Markets Group.
  3. Emmanuel Farhi, 2008. "Rare Disasters and Exchange Rates," 2008 Meeting Papers 47, Society for Economic Dynamics.
  4. Gourio, François, 2008. "Time-series predictability in the disaster model," Finance Research Letters, Elsevier, vol. 5(4), pages 191-203, December.
  5. Dennis Kristensen & Antonio Mele, 2009. "Adding and Subtracting Black-Scholes: A New Approach to Approximating Derivative Prices in Continuous Time Models," CREATES Research Papers 2009-14, School of Economics and Management, University of Aarhus.
  6. JULES H. van BINSBERGEN & RALPH S. J. KOIJEN, 2010. "Predictive Regressions: A Present-Value Approach," Journal of Finance, American Finance Association, vol. 65(4), pages 1439-1471, 08.
  7. John H. Cochrane, 2013. "A Mean-Variance Benchmark for Intertemporal Portfolio Theory," NBER Working Papers 18768, National Bureau of Economic Research, Inc.
  8. Igor Halperin & Andrey Itkin, 2013. "USLV: Unspanned Stochastic Local Volatility Model," Papers 1301.4442, arXiv.org, revised Mar 2013.
  9. 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.
  10. Yu Chen & Thomas Cosimano & Alex Himonas, 2010. "Continuous time one-dimensional asset-pricing models with analytic price–dividend functions," Economic Theory, Springer, vol. 42(3), pages 461-503, March.

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