IDEAS home Printed from https://ideas.repec.org/a/oup/revfin/v9y2005i1p97-137..html
   My bibliography  Save this article

Interpreting Implied Risk-Neutral Densities: The Role of Risk Premia

Author

Listed:
  • Peter Hördahl
  • David Vestin

Abstract

This paper examines differences between risk-neutral and objective probability densities of future interest rates. The identification and quantification of these differences are important when risk-neutral densities (RNDs), such as option-implied RNDs, are used as indicators of actual beliefs of investors. We employ a multi-factor essentially affine modeling framework applied to German time-series and cross-section term structure data in order to identify both the risk-neutral and the objective term structure dynamics. We find important differences between risk-neutral and objective distributions due to risk premia in bond prices. Moreover, the estimated premia vary over time in a quantitatively significant way, which implies that the differences between the objective and the risk-neutral distributions also vary over time. We therefore conclude that one should be cautious in interpreting RNDs in terms of expectations. The method used in this paper provides an alternative approach to identifying objective probabilities of future interest rates.

Suggested Citation

  • Peter Hördahl & David Vestin, 2005. "Interpreting Implied Risk-Neutral Densities: The Role of Risk Premia," Review of Finance, European Finance Association, vol. 9(1), pages 97-137.
    • Handle: RePEc:oup:revfin:v:9:y:2005:i:1:p:97-137.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10679-005-2989-7
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Robert R. Bliss & Nikolaos Panigirtzoglou, 2001. "Recovering risk aversion from options," Working Paper Series WP-01-15, Federal Reserve Bank of Chicago.
    2. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    3. Soderlind, Paul & Svensson, Lars, 1997. "New techniques to extract market expectations from financial instruments," Journal of Monetary Economics, Elsevier, vol. 40(2), pages 383-429, October.
    4. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    5. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    6. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    8. Ait-Sahalia, Yacine & Wang, Yubo & Yared, Francis, 2001. "Do option markets correctly price the probabilities of movement of the underlying asset?," Journal of Econometrics, Elsevier, vol. 102(1), pages 67-110, May.
    9. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    10. Lars E.O. Svensson, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992 - 1994," NBER Working Papers 4871, National Bureau of Economic Research, Inc.
    11. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    12. Peter Hördahl & David Vestin, 2005. "Interpreting Implied Risk-Neutral Densities: The Role of Risk Premia," Review of Finance, Springer, vol. 9(1), pages 97-137, March.
    13. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    14. de Jong, Frank, 2000. "Time Series and Cross-Section Information in Affine Term-Structure Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 300-314, July.
    15. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    16. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    17. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    18. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    19. Duarte, Jefferson., 2003. "Evaluating an Alternative Risk Preference in Affine Term Structure Models," Finance Lab Working Papers flwp_49, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    20. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
    21. Dai, Qiang & Singleton, Kenneth J., 2002. "Expectation puzzles, time-varying risk premia, and affine models of the term structure," Journal of Financial Economics, Elsevier, vol. 63(3), pages 415-441, March.
    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. Jukka Sihvonen & Sami Vähämaa, 2014. "Forward‐Looking Monetary Policy Rules and Option‐Implied Interest Rate Expectations," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(4), pages 346-373, April.
    2. Ascari, Guido & Rankin, Neil, 2007. "Perpetual youth and endogenous labor supply: A problem and a possible solution," Journal of Macroeconomics, Elsevier, vol. 29(4), pages 708-723, December.
    3. Ma, Zong-Gang & Ma, Chao-Qun, 2013. "Pricing catastrophe risk bonds: A mixed approximation method," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 243-254.
    4. Peter Hördahl & David Vestin, 2005. "Interpreting Implied Risk-Neutral Densities: The Role of Risk Premia," Review of Finance, European Finance Association, vol. 9(1), pages 97-137.
    5. Eickholt, Mathias & Entrop, Oliver & Wilkens, Marco, 2014. "Individual investors and suboptimal early exercises in the fixed-income market," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe 14, University of Passau, Faculty of Business and Economics.
    6. Guillermo Benavides Perales & Israel Felipe Mora Cuevas, 2008. "Parametric vs. non-parametric methods for estimating option implied risk-neutral densities: the case of the exchange rate Mexican peso – US dollar," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(1), pages 33-52, May.
    7. Bagnara, Matteo & Jappelli, Ruggero, 2022. "Liquidity derivatives," SAFE Working Paper Series 358, Leibniz Institute for Financial Research SAFE.
    8. William R. Emmons & Aeimit K. Lakdawala & Christopher J. Neely, 2006. "What are the odds? option-based forecasts of FOMC target changes," Review, Federal Reserve Bank of St. Louis, vol. 88(Nov), pages 543-562.
    9. Don H. Kim, 2008. "Zero bound, option-implied PDFs, and term structure models," Finance and Economics Discussion Series 2008-31, Board of Governors of the Federal Reserve System (U.S.).
    10. Schmitz, Jochen & Ledebur, Oliver von, 2012. "The 2007 emerging corn price surge revisited – Was it expected or a large surprise?," 2012 Conference, August 18-24, 2012, Foz do Iguacu, Brazil 123971, International Association of Agricultural Economists.
    11. Eickholt, Mathias & Entrop, Oliver & Wilkens, Marco, 2018. "What makes individual investors exercise early? Empirical evidence from non-tradable fixed-income products," Journal of Banking & Finance, Elsevier, vol. 97(C), pages 318-334.

    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. repec:wyi:journl:002108 is not listed on IDEAS
    2. Chen, Bin & Hong, Yongmiao, 2011. "Generalized spectral testing for multivariate continuous-time models," Journal of Econometrics, Elsevier, vol. 164(2), pages 268-293, October.
    3. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    4. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    5. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    6. Cai, Lili & Swanson, Norman R., 2011. "In- and out-of-sample specification analysis of spot rate models: Further evidence for the period 1982-2008," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 743-764, September.
    7. repec:wyi:journl:002117 is not listed on IDEAS
    8. repec:wyi:journl:002142 is not listed on IDEAS
    9. Bin Chen & Yongmiao Hong, 2013. "Characteristic Function-Based Testing for Multifactor Continuous-Time Markov Models via Nonparametri," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    10. Cai, Zongwu & Hong, Yongmiao, 2003. "Nonparametric Methods in Continuous-Time Finance: A Selective Review," SFB 373 Discussion Papers 2003,15, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    11. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
    12. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    13. Driessen, Joost & Melenberg, Bertrand & Nijman, Theo, 2005. "Testing affine term structure models in case of transaction costs," Journal of Econometrics, Elsevier, vol. 126(1), pages 201-232, May.
    14. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    15. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    16. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    17. Hautsch, Nikolaus & Ou, Yangguoyi, 2012. "Analyzing interest rate risk: Stochastic volatility in the term structure of government bond yields," Journal of Banking & Finance, Elsevier, vol. 36(11), pages 2988-3007.
    18. Christensen, Bent Jesper & Kjær, Mads Markvart & Veliyev, Bezirgen, 2023. "The incremental information in the yield curve about future interest rate risk," Journal of Banking & Finance, Elsevier, vol. 155(C).
    19. Peter Feldhütter & Christian Heyerdahl-Larsen & Philipp Illeditsch, 2018. "Risk Premia and Volatilities in a Nonlinear Term Structure Model [Quadratic term structure models: theory and evidence]," Review of Finance, European Finance Association, vol. 22(1), pages 337-380.
    20. Carverhill, Andrew & Luo, Dan, 2023. "A Bayesian analysis of time-varying jump risk in S&P 500 returns and options," Journal of Financial Markets, Elsevier, vol. 64(C).
    21. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    22. Carrasco, Marine & Chernov, Mikhaël & Florens, Jean-Pierre & Ghysels, Eric, 2000. "Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions," IDEI Working Papers 116, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2002.
    23. Coroneo, Laura & Nyholm, Ken & Vidova-Koleva, Rositsa, 2011. "How arbitrage-free is the Nelson-Siegel model?," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 393-407, June.

    More about this item

    JEL classification:

    • J45 - Labor and Demographic Economics - - Particular Labor Markets - - - Public Sector Labor Markets
    • H7 - Public Economics - - State and Local Government; Intergovernmental Relations

    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:oup:revfin:v:9:y:2005:i:1:p:97-137.. 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: Oxford University Press (email available below). General contact details of provider: https://edirc.repec.org/data/eufaaea.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.