IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v214y2020i2p295-325.html
   My bibliography  Save this article

Nonparametric filtering of conditional state-price densities

Author

Listed:
  • Dalderop, Jeroen

Abstract

This paper studies the use of noisy high-frequency data to estimate the time-varying state-price density implicit in European option prices. A dynamic kernel estimator of the conditional pricing function and its derivatives is proposed that can be used for model-free risk measurement. Infill asymptotic theory is derived that applies when the pricing function is either smoothly varying or driven by diffusive state variables. Trading times and moneyness levels are modeled by marked point processes that capture intraday trading patterns. A simulation study investigates the performance of the estimator using a varying plug-in bandwidth in various scenarios. Empirical analysis using S&P 500 E-mini European option quotes reveals significant time-variation at intraday frequencies. An application towards delta- and minimum variance-hedging further illustrates the use of the estimator.

Suggested Citation

  • Dalderop, Jeroen, 2020. "Nonparametric filtering of conditional state-price densities," Journal of Econometrics, Elsevier, vol. 214(2), pages 295-325.
    • Handle: RePEc:eee:econom:v:214:y:2020:i:2:p:295-325
    DOI: 10.1016/j.jeconom.2019.05.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030440761930168X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2019.05.022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Markus Bibinger & Nikolaus Hautsch & Peter Malec & Markus Reiss, 2019. "Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 419-435, July.
    2. Audrino, Francesco & Fengler, Matthias R., 2015. "Are classical option pricing models consistent with observed option second-order moments? Evidence from high-frequency data," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 46-63.
    3. Yatchew, Adonis & Hardle, Wolfgang, 2006. "Nonparametric state price density estimation using constrained least squares and the bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 579-599, August.
    4. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    5. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    6. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    7. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    8. Irène Gijbels & Alexandre Lambert & Peihua Qiu, 2007. "Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 235-272, June.
    9. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    10. Pawlas, Zbynek, 2009. "Empirical distributions in marked point processes," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4194-4209, December.
    11. Zhang, Xibin & Brooks, Robert D. & King, Maxwell L., 2009. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Journal of Econometrics, Elsevier, vol. 153(1), pages 21-32, November.
    12. Vergote, Olivier & Puigvert Gutiérrez, Josep Maria, 2012. "Interest rate expectations and uncertainty during ECB Governing Council days: Evidence from intraday implied densities of 3-month EURIBOR," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2804-2823.
    13. Andersen, Torben G. & Bondarenko, Oleg & Todorov, Viktor & Tauchen, George, 2015. "The fine structure of equity-index option dynamics," Journal of Econometrics, Elsevier, vol. 187(2), pages 532-546.
    14. Beber, Alessandro & Brandt, Michael W., 2006. "The effect of macroeconomic news on beliefs and preferences: Evidence from the options market," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 1997-2039, November.
    15. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    16. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    17. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
    18. Alexander, Carol & Nogueira, Leonardo M., 2007. "Model-free hedge ratios and scale-invariant models," Journal of Banking & Finance, Elsevier, vol. 31(6), pages 1839-1861, June.
    19. Härdle, Wolfgang & Hlávka, Zdenek, 2009. "Dynamics of state price densities," Journal of Econometrics, Elsevier, vol. 150(1), pages 1-15, May.
    20. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Discussion Papers (ECON - Département des Sciences Economiques) 2006039, Université catholique de Louvain, Département des Sciences Economiques.
    21. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, vol. 179(2), pages 158-177.
    22. Michael Vogt, 2012. "Nonparametric regression for locally stationary time series," CeMMAP working papers CWP22/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    23. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    24. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    25. Fan, Jianqing & Mancini, Loriano, 2009. "Option Pricing With Model-Guided Nonparametric Methods," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1351-1372.
    26. Zu, Yang & Peter Boswijk, H., 2014. "Estimating spot volatility with high-frequency financial data," Journal of Econometrics, Elsevier, vol. 181(2), pages 117-135.
    27. Jia Li & Dacheng Xiu, 2016. "Generalized Method of Integrated Moments for High‐Frequency Data," Econometrica, Econometric Society, vol. 84, pages 1613-1633, July.
    28. Melanie Birke & Kay F. Pilz, 2009. "Nonparametric Option Pricing with No-Arbitrage Constraints," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 53-76, Spring.
    29. Hall, Peter & Schucany, William R., 1989. "A local cross-validation algorithm," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 109-117, June.
    30. Kristensen, Dennis, 2010. "Nonparametric Filtering Of The Realized Spot Volatility: A Kernel-Based Approach," Econometric Theory, Cambridge University Press, vol. 26(1), pages 60-93, February.
    31. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, June.
    32. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    33. Fengler, Matthias R. & Hin, Lin-Yee, 2015. "Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints," Journal of Econometrics, Elsevier, vol. 184(2), pages 242-261.
    34. Per Aslak Mykland & Lan Zhang, 2006. "ANOVA for diffusions and It\^{o} processes," Papers math/0611274, arXiv.org.
    35. Chen, Song Xi & Xu, Zheng, 2014. "On implied volatility for options—Some reasons to smile and more to correct," Journal of Econometrics, Elsevier, vol. 179(1), pages 1-15.
    36. Birru, Justin & Figlewski, Stephen, 2012. "Anatomy of a meltdown: The risk neutral density for the S&P 500 in the fall of 2008," Journal of Financial Markets, Elsevier, vol. 15(2), pages 151-180.
    37. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
    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. Evgenii Vladimirov, 2023. "iCOS: Option-Implied COS Method," Papers 2309.00943, arXiv.org, revised Feb 2024.
    2. Ana M. Monteiro & Antonio A. F. Santos, 2020. "Conditional risk-neutral density from option prices by local polynomial kernel smoothing with no-arbitrage constraints," Review of Derivatives Research, Springer, vol. 23(1), pages 41-61, April.
    3. Ana M. Monteiro & António A. F. Santos, 2022. "Option prices for risk‐neutral density estimation using nonparametric methods through big data and large‐scale problems," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(1), pages 152-171, January.

    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. Fengler, Matthias & Hin, Lin-Yee, 2011. "Semi-nonparametric estimation of the call price surface under strike and time-to-expiry no-arbitrage constraints," Economics Working Paper Series 1136, University of St. Gallen, School of Economics and Political Science, revised May 2013.
    2. Ana M. Monteiro & Antonio A. F. Santos, 2020. "Conditional risk-neutral density from option prices by local polynomial kernel smoothing with no-arbitrage constraints," Review of Derivatives Research, Springer, vol. 23(1), pages 41-61, April.
    3. Lu, Junwen & Qu, Zhongjun, 2021. "Sieve estimation of option-implied state price density," Journal of Econometrics, Elsevier, vol. 224(1), pages 88-112.
    4. Karl Härdle, Wolfgang & López-Cabrera, Brenda & Teng, Huei-Wen, 2015. "State price densities implied from weather derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 106-125.
    5. Arindam Kundu & Sumit Kumar & Nutan Kumar Tomar, 2019. "Option Implied Risk-Neutral Density Estimation: A Robust and Flexible Method," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 705-728, August.
    6. Fengler, Matthias R. & Hin, Lin-Yee, 2015. "Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints," Journal of Econometrics, Elsevier, vol. 184(2), pages 242-261.
    7. Robert A. Jarrow & Simon S. Kwok, 2021. "Inferring financial bubbles from option data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(7), pages 1013-1046, November.
    8. Grith, Maria & Härdle, Wolfgang Karl & Schienle, Melanie, 2010. "Nonparametric estimation of risk-neutral densities," SFB 649 Discussion Papers 2010-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    10. repec:hum:wpaper:sfb649dp2013-026 is not listed on IDEAS
    11. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    12. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    13. Polkovnichenko, Valery & Zhao, Feng, 2013. "Probability weighting functions implied in options prices," Journal of Financial Economics, Elsevier, vol. 107(3), pages 580-609.
    14. René Garcia & Richard Luger & Éric Renault, 2005. "Viewpoint: Option prices, preferences, and state variables," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(1), pages 1-27, February.
    15. Arindam Kundu & Sumit Kumar & Nutan Kumar Tomar, 2024. "A Semi-Closed Form Approximation of Arbitrage-Free Call Option Price Surface," Computational Economics, Springer;Society for Computational Economics, vol. 63(4), pages 1431-1457, April.
    16. repec:wyi:journl:002108 is not listed on IDEAS
    17. Xixuan Han & Boyu Wei & Hailiang Yang, 2018. "Index Options And Volatility Derivatives In A Gaussian Random Field Risk-Neutral Density Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-41, June.
    18. Haitao Li & Feng Zhao, 2009. "Nonparametric Estimation of State-Price Densities Implicit in Interest Rate Cap Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4335-4376, November.
    19. Andrea Barletta & Paolo Santucci de Magistris & Francesco Violante, 2016. "Retrieving Risk-Neutral Densities Embedded in VIX Options: a Non-Structural Approach," CREATES Research Papers 2016-20, Department of Economics and Business Economics, Aarhus University.
    20. Garcia, Rene & Luger, Richard & Renault, Eric, 2003. "Empirical assessment of an intertemporal option pricing model with latent variables," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 49-83.
    21. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, vol. 173(1), pages 57-82.
    22. repec:hum:wpaper:sfb649dp2010-021 is not listed on IDEAS
    23. René Garcia & Richard Luger & Eric Renault, 2001. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables (Note : Nouvelle version Février 2002)," CIRANO Working Papers 2001s-02, CIRANO.

    More about this item

    Keywords

    Option pricing; Kernel regression; High-frequency data; Random sampling times;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:eee:econom:v:214:y:2020:i:2:p:295-325. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.