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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.

Suggested Citation

  • Xavier Gabaix, 2007. "Linearity-Generating Processes: A Modelling Tool Yielding Closed Forms for Asset Prices," NBER Working Papers 13430, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:13430
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    References listed on IDEAS

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    Cited by:

    1. 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, vol. 102(2), pages 390-415.
    2. John H. Cochrane, 2014. "A Mean-Variance Benchmark for Intertemporal Portfolio Theory," Journal of Finance, American Finance Association, vol. 69(1), pages 1-49, February.
    3. Damir Filipovic & Martin Larsson & Anders B. Trolle, 2018. "On the Relation Between Linearity-Generating Processes and Linear-Rational Models," Papers 1806.03153, arXiv.org.
    4. Gourieroux, C. & Monfort, A., 2013. "Linear-price term structure models," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 24-41.
    5. Roger Farmer, 2014. "Asset Prices in a Lifecycle Economy," NBER Working Papers 19958, National Bureau of Economic Research, Inc.
    6. Jerry Tsai & Jessica A. Wachter, 2015. "Disaster Risk and its Implications for Asset Pricing," NBER Working Papers 20926, National Bureau of Economic Research, Inc.
    7. Gourio, François, 2008. "Time-series predictability in the disaster model," Finance Research Letters, Elsevier, vol. 5(4), pages 191-203, December.
    8. 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, August.
    9. Emmanuel Farhi & Xavier Gabaix, "undated". "Rare Disasters and Exchange Rates," Working Paper 71001, Harvard University OpenScholar.
    10. Hanno Lustig, "undated". "The Wealth-Consumption Ratio: A Litmus Test for Consumption-based Asset Pricing Models," UCLA Economics Online Papers 420, UCLA Department of Economics.
    11. Christian Julliard & Anisha Ghosh, 2012. "Can Rare Events Explain the Equity Premium Puzzle?," Review of Financial Studies, Society for Financial Studies, vol. 25(10), pages 3037-3076.
    12. Yu Chen & Thomas Cosimano & Alex Himonas, 2010. "Continuous time one-dimensional asset-pricing models with analytic price–dividend functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 461-503, March.
    13. Marco Bonomo & René Garcia & Nour Meddahi & Roméo Tédongap, 2011. "Generalized Disappointment Aversion, Long-run Volatility Risk, and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 24(1), pages 82-122.
    14. Vayanos, Dimitri & Vila, Jean-Luc, 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.
    15. 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.
    16. Igor Halperin & Andrey Itkin, 2013. "USLV: Unspanned Stochastic Local Volatility Model," Papers 1301.4442, arXiv.org, revised Mar 2013.
    17. 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.

    More about this item

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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