IDEAS home Printed from https://ideas.repec.org/a/wly/jfutmk/v42y2022i3p365-388.html
   My bibliography  Save this article

Bakshi, Kapadia, and Madan (2003) risk‐neutral moment estimators: An affine jump‐diffusion approach

Author

Listed:
  • Pakorn Aschakulporn
  • Jin E. Zhang

Abstract

This is the first study of the errors in the Bakshi, Kapadia, and Madan risk‐neutral moment estimators under the Duffie, Pan, and Singleton affine jump‐diffusion model benchmarked against their true values. This is accomplished by extending the exact solutions from Zhen and Zhang. To mitigate errors in skewness, interpolating the implied volatility curve linearly and applying constant extrapolation to have a step size of $1 and strikes ranging from a quarter to quadruple the forward price should yield skewness values with errors less than 1 0 − 3, based on simulated data using parameters calibrated with the S&P 500 index during 2020.

Suggested Citation

  • Pakorn Aschakulporn & Jin E. Zhang, 2022. "Bakshi, Kapadia, and Madan (2003) risk‐neutral moment estimators: An affine jump‐diffusion approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(3), pages 365-388, March.
  • Handle: RePEc:wly:jfutmk:v:42:y:2022:i:3:p:365-388
    DOI: 10.1002/fut.22280
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/fut.22280
    Download Restriction: no

    File URL: https://libkey.io/10.1002/fut.22280?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. Jin E. Zhang & Fang Zhen & Xiaoxia Sun & Huimin Zhao, 2017. "The Skewness Implied in the Heston Model and Its Application," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(3), pages 211-237, March.
    2. Jennifer Conrad & Robert F. Dittmar & Eric Ghysels, 2013. "Ex Ante Skewness and Expected Stock Returns," Journal of Finance, American Finance Association, vol. 68(1), pages 85-124, February.
    3. Erwan Morellec & Alexei Zhdanov, 2019. "Product Market Competition and Option Prices," Review of Financial Studies, Society for Financial Studies, vol. 32(11), pages 4343-4386.
    4. Chatrath, Arjun & Miao, Hong & Ramchander, Sanjay & Wang, Tianyang, 2016. "An examination of the flow characteristics of crude oil: Evidence from risk-neutral moments," Energy Economics, Elsevier, vol. 54(C), pages 213-223.
    5. Birru, Justin & Wang, Baolian, 2016. "Nominal price illusion," Journal of Financial Economics, Elsevier, vol. 119(3), pages 578-598.
    6. Jennifer Conrad & Robert F Dittmar & Allaudeen Hameed, 0. "Implied Default Probabilities and Losses Given Default from Option Prices," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 18(3), pages 629-652.
    7. Chang, Bo Young & Christoffersen, Peter & Jacobs, Kris, 2013. "Market skewness risk and the cross section of stock returns," Journal of Financial Economics, Elsevier, vol. 107(1), pages 46-68.
    8. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    9. Jing-zhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time-Changed Lévy Processes," Journal of Finance, American Finance Association, vol. 59(3), pages 1405-1440, June.
    10. Vasquez, Aurelio, 2017. "Equity Volatility Term Structures and the Cross Section of Option Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 52(6), pages 2727-2754, December.
    11. Xingguo Luo & Jin E. Zhang, 2012. "The Term Structure of VIX," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(12), pages 1092-1123, December.
    12. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    13. Jennifer Conrad & Robert F Dittmar & Allaudeen Hameed, 2020. "Implied Default Probabilities and Losses Given Default from Option Prices," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 18(3), pages 629-652.
    14. George J. Jiang & John L. Knight, 2010. "ECF estimation of Markov models where the transition density is unknown," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 245-270, July.
    15. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    16. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    17. Christopher S. Jones & Joshua Shemesh, 2018. "Option Mispricing around Nontrading Periods," Journal of Finance, American Finance Association, vol. 73(2), pages 861-900, April.
    18. 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.
    19. P. Carr & D. Madan, 2001. "Optimal positioning in derivative securities," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 19-37.
    20. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    21. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    22. Neumann, Michael & Skiadopoulos, George, 2013. "Predictable Dynamics in Higher-Order Risk-Neutral Moments: Evidence from the S&P 500 Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(3), pages 947-977, June.
    23. Gurdip Bakshi & Dilip Madan, 2006. "A Theory of Volatility Spreads," Management Science, INFORMS, vol. 52(12), pages 1945-1956, December.
    24. 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.
    25. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    26. Byun, Suk-Joon & Kim, Da-Hea, 2016. "Gambling preference and individual equity option returns," Journal of Financial Economics, Elsevier, vol. 122(1), pages 155-174.
    27. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    28. Jiang, George J & Knight, John L, 2002. "Estimation of Continuous-Time Processes via the Empirical Characteristic Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 198-212, April.
    29. 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.
    30. Fabian Hollstein & Marcel Prokopczuk & Chardin Wese Simen, 2020. "The Conditional Capital Asset Pricing Model Revisited: Evidence from High-Frequency Betas," Management Science, INFORMS, vol. 66(6), pages 2474-2494, June.
    31. Przemysław S. Stilger & Alexandros Kostakis & Ser-Huang Poon, 2017. "What Does Risk-Neutral Skewness Tell Us About Future Stock Returns?," Management Science, INFORMS, vol. 63(6), pages 1814-1834, June.
    32. Ruan, Xinfeng & Zhang, Jin E., 2018. "Equilibrium variance risk premium in a cost-free production economy," Journal of Economic Dynamics and Control, Elsevier, vol. 96(C), pages 42-60.
    33. 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)

    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. Ruan, Xinfeng & Zhang, Jin E., 2018. "Risk-neutral moments in the crude oil market," Energy Economics, Elsevier, vol. 72(C), pages 583-600.
    3. Gurdip Bakshi & Charles Cao & Zhaodong (Ken) Zhong, 2021. "Assessing models of individual equity option prices," Review of Quantitative Finance and Accounting, Springer, vol. 57(1), pages 1-28, July.
    4. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2009. "Exploring Time-Varying Jump Intensities: Evidence from S&P500 Returns and Options," CIRANO Working Papers 2009s-34, CIRANO.
    5. 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.
    6. Pakorn Aschakulporn & Jin E. Zhang, 2022. "Bakshi, Kapadia, and Madan (2003) risk-neutral moment estimators: A Gram–Charlier density approach," Review of Derivatives Research, Springer, vol. 25(3), pages 233-281, October.
    7. Biao Guo & Hai Lin, 2020. "Volatility and jump risk in option returns," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(11), pages 1767-1792, November.
    8. Pacati, Claudio & Pompa, Gabriele & Renò, Roberto, 2018. "Smiling twice: The Heston++ model," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 185-206.
    9. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    10. Shin-Yun Wang & Ming-Che Chuang & Shih-Kuei Lin & So-De Shyu, 2021. "Option pricing under stock market cycles with jump risks: evidence from the S&P 500 index," Review of Quantitative Finance and Accounting, Springer, vol. 56(1), pages 25-51, January.
    11. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
    12. Sanjay K. Nawalkha & Xiaoyang Zhuo, 2020. "A Theory of Equivalent Expectation Measures for Contingent Claim Returns," Papers 2006.15312, arXiv.org, revised May 2022.
    13. Erik Vogt, 2014. "Option-implied term structures," Staff Reports 706, Federal Reserve Bank of New York.
    14. Bjørn Eraker & Aoxiang Yang, 2022. "The Price of Higher Order Catastrophe Insurance: The Case of VIX Options," Journal of Finance, American Finance Association, vol. 77(6), pages 3289-3337, December.
    15. Jiling Cao & Xinfeng Ruan & Wenjun Zhang, 2020. "Inferring information from the S&P 500, CBOE VIX, and CBOE SKEW indices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 945-973, June.
    16. Eva Ferreira & Mónica Gago & Angel León & Gonzalo Rubio, 2005. "An empirical comparison of the performance of alternative option pricing models," Investigaciones Economicas, Fundación SEPI, vol. 29(3), pages 483-523, September.
    17. Yan, Shu, 2011. "Jump risk, stock returns, and slope of implied volatility smile," Journal of Financial Economics, Elsevier, vol. 99(1), pages 216-233, January.
    18. Nawalkha, Sanjay K & Zhuo, Xiaoyang, 2020. "A Theory of Equivalent Expectation Measures for Expected Prices of Contingent Claims," OSF Preprints hsxtu, Center for Open Science.
    19. Li, Junye & Favero, Carlo & Ortu, Fulvio, 2012. "A spectral estimation of tempered stable stochastic volatility models and option pricing," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3645-3658.
    20. Dario Alitab & Giacomo Bormetti & Fulvio Corsi & Adam A. Majewski, 2019. "A realized volatility approach to option pricing with continuous and jump variance components," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 639-664, December.

    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:42:y:2022:i:3:p:365-388. 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.