IDEAS home Printed from https://ideas.repec.org/p/fip/fedgfe/2014-71.html
   My bibliography  Save this paper

Solving asset pricing models with stochastic volatility

Author

Abstract

This paper provides a closed-form solution for the price-dividend ratio in a standard asset pricing model with stochastic volatility. The solution is useful in allowing comparisons among numerical methods used to approximate the non-trivial closed-form.

Suggested Citation

  • Oliver de Groot, 2014. "Solving asset pricing models with stochastic volatility," Finance and Economics Discussion Series 2014-71, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2014-71
    as

    Download full text from publisher

    File URL: http://www.federalreserve.gov/econresdata/feds/2014/files/201471pap.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Burnside, Craig, 1998. "Solving asset pricing models with Gaussian shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 329-340, March.
    2. Collard, Fabrice & Fève, Patrick & Ghattassi, Imen, 2006. "A Note On The Exact Solution Of Asset Pricing Models With Habit Persistence," Macroeconomic Dynamics, Cambridge University Press, vol. 10(2), pages 273-283, April.
    3. Tsionas, Efthymios G., 2003. "Exact solution of asset pricing models with arbitrary shock distributions," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 843-851, March.
    4. 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.
    5. Alejandro Justiniano & Giorgio E. Primiceri, 2008. "The Time-Varying Volatility of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 98(3), pages 604-641, June.
    6. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," The Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
    7. Martin Andreasen, 2012. "On the Effects of Rare Disasters and Uncertainty Shocks for Risk Premia in Non-Linear DSGE Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(3), pages 295-316, July.
    8. Anh Le & Kenneth J. Singleton & Qiang Dai, 2010. "Discrete-Time Affine-super-ℚ Term Structure Models with Generalized Market Prices of Risk," The Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2184-2227.
    9. 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.
    10. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    11. Jesús Fernández-Villaverde & Pablo Guerrón-Quintana & Keith Kuester & Juan Rubio-Ramírez, 2015. "Fiscal Volatility Shocks and Economic Activity," American Economic Review, American Economic Association, vol. 105(11), pages 3352-3384, November.
    12. Nick Bloom & Stephen Bond & John Van Reenen, 2007. "Uncertainty and Investment Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 391-415.
    13. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1997. "Estimation of stochastic volatility models with diagnostics," Journal of Econometrics, Elsevier, vol. 81(1), pages 159-192, November.
    14. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters, in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230, National Bureau of Economic Research, Inc.
    15. Bidarkota, Prasad V. & McCulloch, J. Huston, 2003. "Consumption asset pricing with stable shocks--exploring a solution and its implications for mean equity returns," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 399-421, January.
    16. Glenn D. Rudebusch & Eric T. Swanson, 2012. "The Bond Premium in a DSGE Model with Long-Run Real and Nominal Risks," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(1), pages 105-143, January.
    17. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    18. 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, May.
    19. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    20. Labadie, Pamela, 1989. "Stochastic inflation and the equity premium," Journal of Monetary Economics, Elsevier, vol. 24(2), pages 277-298, September.
    21. Dario Caldara & Jesus Fernandez-Villaverde & Juan Rubio-Ramirez & Wen Yao, 2012. "Computing DSGE Models with Recursive Preferences and Stochastic Volatility," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 188-206, April.
    22. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    23. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    24. Geweke, John, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 397-399, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Juan M. Londono & Nancy R. Xu, 2021. "The Global Determinants of International Equity Risk Premiums," International Finance Discussion Papers 1318, Board of Governors of the Federal Reserve System (U.S.).
    2. Levintal, Oren, 2017. "Fifth-order perturbation solution to DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 1-16.
    3. A. Ronald Gallant & George Tauchen, 2021. "Cash Flows Discounted Using a Model-Free SDF Extracted under a Yield Curve Prior," JRFM, MDPI, vol. 14(3), pages 1-15, March.
    4. Michael Curran & Adnan Velic, 2020. "Interest rate volatility and macroeconomic dynamics: Heterogeneity matters," Review of International Economics, Wiley Blackwell, vol. 28(4), pages 957-975, September.
    5. Lott, Sherwin, 2019. "Perturbations in DSGE models: An odd derivatives theorem," Journal of Economic Dynamics and Control, Elsevier, vol. 106(C), pages 1-1.
    6. Jules Tinang & Nour Meddahi, 2016. "GMM estimation of the Long Run Risks model," 2016 Meeting Papers 1107, Society for Economic Dynamics.
    7. Michael Patrick Curran & Adnan Velic, 2017. "Interest Rate Volatility And Macroeconomic Dynamics: A Cross-Country Analysis," Villanova School of Business Department of Economics and Statistics Working Paper Series 35, Villanova School of Business Department of Economics and Statistics.
    8. Toda, Alexis Akira, 2017. "Huggett economies with multiple stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 77-90.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hong Lan & Alexander Meyer-Gohde, 2013. "Decomposing Risk in Dynamic Stochastic General Equilibrium," SFB 649 Discussion Papers SFB649DP2013-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. 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.
    3. Walter Pohl & Karl Schmedders & Ole Wilms, 2018. "Higher Order Effects in Asset Pricing Models with Long‐Run Risks," Journal of Finance, American Finance Association, vol. 73(3), pages 1061-1111, June.
    4. Isoré, Marlène & Szczerbowicz, Urszula, 2017. "Disaster risk and preference shifts in a New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 97-125.
    5. Martin Andreasen, 2012. "On the Effects of Rare Disasters and Uncertainty Shocks for Risk Premia in Non-Linear DSGE Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(3), pages 295-316, July.
    6. Lorenzo Bretscher & Alex Hsu & Andrea Tamoni, 2019. "Response of the Macroeconomy to Uncertainty Shocks:the Risk Premium Channel," 2019 Meeting Papers 1567, Society for Economic Dynamics.
    7. Jesús Fernández-Villaverde, 2010. "The econometrics of DSGE models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 1(1), pages 3-49, March.
    8. Fernández-Villaverde, Jesús & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Estimating dynamic equilibrium models with stochastic volatility," Journal of Econometrics, Elsevier, vol. 185(1), pages 216-229.
    9. Marcelo Ferman, 2011. "Switching Monetary Policy Regimes and the Nominal Term Structure," FMG Discussion Papers dp678, Financial Markets Group.
    10. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana, 2020. "Uncertainty Shocks and Business Cycle Research," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 37, pages 118-166, August.
    11. Gianni Amisano & Oreste Tristani, 2019. "Uncertainty Shocks, Monetary Policy and Long-Term Interest Rates," Finance and Economics Discussion Series 2019-024, Board of Governors of the Federal Reserve System (U.S.).
    12. Meyer-Gohde, Alexander, 2015. "Risk-Sensitive Linear Approximations," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113057, Verein für Socialpolitik / German Economic Association.
    13. Martin M. Andreasen & Kasper Jørgensen, 2016. "Explaining Asset Prices with Low Risk Aversion and Low Intertemporal Substitution," CREATES Research Papers 2016-16, Department of Economics and Business Economics, Aarhus University.
    14. Cui, Liyuan & Hong, Yongmiao & Li, Yingxing, 2021. "Solving Euler equations via two-stage nonparametric penalized splines," Journal of Econometrics, Elsevier, vol. 222(2), pages 1024-1056.
    15. Andreasen Martin M. & Zabczyk Pawel, 2015. "Efficient bond price approximations in non-linear equilibrium-based term structure models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(1), pages 1-33, February.
    16. Bekaert, Geert & Engstrom, Eric & Grenadier, Steven R., 2010. "Stock and bond returns with Moody Investors," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 867-894, December.
    17. Ravi Bansal, 2007. "Long-run risks and financial markets," Review, Federal Reserve Bank of St. Louis, vol. 89(Jul), pages 283-300.
    18. Bidarkota, Prasad V. & Dupoyet, Brice V. & McCulloch, J. Huston, 2009. "Asset pricing with incomplete information and fat tails," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1314-1331, June.
    19. Aldrich Eric Mark & Kung Howard, 2021. "Computational Methods for Production-Based Asset Pricing Models with Recursive Utility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(1), pages 1-26, February.
    20. Josué Diwambuena & Jean-Paul K. Tsasa, 2021. "The Real Effects of Uncertainty Shocks: New Evidence from Linear and Nonlinear SVAR Models," BEMPS - Bozen Economics & Management Paper Series BEMPS87, Faculty of Economics and Management at the Free University of Bozen.

    More about this item

    Keywords

    Endowment model; price-dividend ratio; closed-form solution;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:fedgfe:2014-71. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ryan Wolfslayer ; Keisha Fournillier (email available below). General contact details of provider: https://edirc.repec.org/data/frbgvus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.