IDEAS home Printed from https://ideas.repec.org/a/wly/jfutmk/v39y2019i12p1587-1612.html
   My bibliography  Save this article

Monte Carlo analysis of methods for extracting risk‐neutral densities with affine jump diffusions

Author

Listed:
  • Shan Lu

Abstract

This article compares several widely used and recently developed methods to extract risk‐neutral densities (RNDs) from option prices in terms of estimation accuracy. It shows that the positive convolution approximation method consistently yields the most accurate RND estimates, and is insensitive to the discreteness of option prices. RND methods are less likely to produce accurate RND estimates when the underlying process incorporates jumps and when estimations are performed on sparse data, especially for short time‐to‐maturities, though sensitivity to the discreteness of the data differs across different methods.

Suggested Citation

  • Shan Lu, 2019. "Monte Carlo analysis of methods for extracting risk‐neutral densities with affine jump diffusions," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(12), pages 1587-1612, December.
    • Handle: RePEc:wly:jfutmk:v:39:y:2019:i:12:p:1587-1612
    DOI: 10.1002/fut.22049
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/fut.22049
    Download Restriction: no
    File URL: https://libkey.io/10.1002/fut.22049?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
    ---><---

    References listed on IDEAS

    as
    1. Ivanova, Vesela & Puigvert Gutiérrez, Josep Maria, 2014. "Interest rate forecasts, state price densities and risk premium from Euribor options," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 210-223.
    2. Sherrick, Bruce J & Irwin, Scott H & Forster, D Lynn, 1996. "An Examination of Option-Implied S&P 500 Futures Price Distributions," The Financial Review, Eastern Finance Association, vol. 31(3), pages 667-694, August.
    3. Bødskov Andersen, Allan & Wagener, Tom, 2002. "Extracting risk neutral probability densities by fitting implied volatility smiles: some methodological points and an application to the 3M Euribor futures option prices," Working Paper Series 198, European Central Bank.
    4. van Wijnbergen, Sweder & Olijslagers, Stan & Petersen, Annelie & de Vette, Nander, 2018. "What Option Prices tell us about the ECB's Unconventional Monetary Policies," CEPR Discussion Papers 13371, C.E.P.R. Discussion Papers.
    5. Bookstaber, Richard M & McDonald, James B, 1987. "A General Distribution for Describing Security Price Returns," The Journal of Business, University of Chicago Press, vol. 60(3), pages 401-424, July.
    6. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    7. Oleg Bondarenko, 2003. "Statistical Arbitrage and Securities Prices," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 875-919, July.
    8. Satchell, Stephen & Knight, John, 2007. "Forecasting Volatility in the Financial Markets," Elsevier Monographs, Elsevier, edition 3, number 9780750669429.
    9. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    10. 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.
    11. Bali, Turan G. & Murray, Scott, 2013. "Does Risk-Neutral Skewness Predict the Cross-Section of Equity Option Portfolio Returns?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(4), pages 1145-1171, August.
    12. Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, February.
    13. Robert J. Ritchey, 1990. "Call Option Valuation For Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-296, December.
    14. Shan Lu, 2019. "Testing the Predictive Ability of Corridor Implied Volatility Under GARCH Models," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(2), pages 129-168, June.
    15. André Santos & João Guerra, 2015. "Implied Risk Neutral Densities From Option Prices: Hypergeometric, Spline, Lognormal, and Edgeworth Functions," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(7), pages 655-678, July.
    16. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    17. Steve Ross, 2015. "The Recovery Theorem," Journal of Finance, American Finance Association, vol. 70(2), pages 615-648, April.
    18. Ritchey, Robert J, 1990. "Call Option Valuation for Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-296, Winter.
    19. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    20. 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.
    21. Rockinger, Michael & Jondeau, Eric, 2002. "Entropy densities with an application to autoregressive conditional skewness and kurtosis," Journal of Econometrics, Elsevier, vol. 106(1), pages 119-142, January.
    22. Ruijun Bu & Kaddour Hadri, 2007. "Estimating option implied risk-neutral densities using spline and hypergeometric functions," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 216-244, July.
    23. Bliss, Robert R. & Panigirtzoglou, Nikolaos, 2002. "Testing the stability of implied probability density functions," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 381-422, March.
    24. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, vol. 179(2), pages 158-177.
    25. Abadir, Karim M. & Rockinger, Michael, 2003. "Density Functionals, With An Option-Pricing Application," Econometric Theory, Cambridge University Press, vol. 19(5), pages 778-811, October.
    26. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
    27. Wan-Ni Lai, 2014. "Comparison of methods to estimate option implied risk-neutral densities," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1839-1855, October.
    28. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
    29. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    30. Stephen Figlewski, 2018. "Risk-Neutral Densities: A Review," Annual Review of Financial Economics, Annual Reviews, vol. 10(1), pages 329-359, November.
    31. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. Rompolis, Leonidas S., 2010. "Retrieving risk neutral densities from European option prices based on the principle of maximum entropy," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 918-937, December.
    4. Fabozzi, Frank J. & Leccadito, Arturo & Tunaru, Radu S., 2014. "Extracting market information from equity options with exponential Lévy processes," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 125-141.
    5. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    6. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    7. Shi-jie Jiang & Mujun Lei & Cheng-Huang Chung, 2018. "An Improvement of Gain-Loss Price Bounds on Options Based on Binomial Tree and Market-Implied Risk-Neutral Distribution," Sustainability, MDPI, vol. 10(6), pages 1-17, June.
    8. Sirio Aramonte & Mohammad R. Jahan-Parvar & Samuel Rosen & John W. Schindler, 2022. "Firm-Specific Risk-Neutral Distributions with Options and CDS," Management Science, INFORMS, vol. 68(9), pages 7018-7033, September.
    9. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    10. Stylianos Perrakis, 2022. "From innovation to obfuscation: continuous time finance fifty years later," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 36(3), pages 369-401, September.
    11. Almeida, Caio & Freire, Gustavo, 2022. "Pricing of index options in incomplete markets," Journal of Financial Economics, Elsevier, vol. 144(1), pages 174-205.
    12. Shackleton, Mark B. & Taylor, Stephen J. & Yu, Peng, 2010. "A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2678-2693, November.
    13. 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.
    14. Maria Kyriacou & Jose Olmo & Marius Strittmatter, 2021. "Optimal portfolio allocation using option‐implied information," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(2), pages 266-285, February.
    15. Healy, J.V. & Gregoriou, A. & Hudson, R., 2018. "Test of recent advances in extracting information from option prices," International Review of Financial Analysis, Elsevier, vol. 56(C), pages 292-302.
    16. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    17. Datta, Deepa Dhume & Londono, Juan M. & Ross, Landon J., 2017. "Generating options-implied probability densities to understand oil market events," Energy Economics, Elsevier, vol. 64(C), pages 440-457.
    18. Liao, Wen Ju & Sung, Hao-Chang, 2020. "Implied risk aversion and pricing kernel in the FTSE 100 index," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    19. Felix Brinkmann & Olaf Korn, 2018. "Risk-adjusted option-implied moments," Review of Derivatives Research, Springer, vol. 21(2), pages 149-173, July.
    20. Gagnon, Marie-Hélène & Power, Gabriel J. & Toupin, Dominique, 2016. "International stock market cointegration under the risk-neutral measure," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 243-255.

    More about this item

    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:wly:jfutmk:v:39:y:2019:i:12:p:1587-1612. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/0270-7314/ .

    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.