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Solving asset pricing models with stochastic volatility

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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
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    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.
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    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.
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    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.
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    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.
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    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)

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    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. Solórzano Andrade, Gustavo & Parra-Alvarez, Juan Carlos, 2024. "Risk sensitive linear approximations," Economics Letters, Elsevier, vol. 238(C).
    3. Lott, Sherwin, 2019. "Perturbations in DSGE models: An odd derivatives theorem," Journal of Economic Dynamics and Control, Elsevier, vol. 106(C), pages 1-1.
    4. Levintal, Oren, 2017. "Fifth-order perturbation solution to DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 1-16.
    5. Jules Tinang & Nour Meddahi, 2016. "GMM estimation of the Long Run Risks model," 2016 Meeting Papers 1107, Society for Economic Dynamics.
    6. 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.
    7. Toda, Alexis Akira, 2017. "Huggett economies with multiple stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 77-90.
    8. 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.
    9. Stachurski, John & Wilms, Ole & Zhang, Junnan, 2024. "Asset pricing with time preference shocks: Existence and uniqueness," Journal of Economic Theory, Elsevier, vol. 216(C).
    10. Stachurski, John & Wilms, Ole & Zhang, Junnan, 2024. "Asset pricing with time preference shocks: Existence and uniqueness," Other publications TiSEM 29da00af-3cca-4717-aa55-a, Tilburg University, School of Economics and Management.
    11. 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.

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    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

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