IDEAS home Printed from https://ideas.repec.org/a/kap/annfin/v15y2019i4d10.1007_s10436-018-0341-4.html
   My bibliography  Save this article

Semi-nonparametric approximation and index options

Author

Listed:
  • Julia Jiang

    (University of North Carolina at Charlotte)

  • Weidong Tian

    (University of North Carolina at Charlotte)

Abstract

In an arbitrage-free securities market, all state-contingent claims and the stochastic discount factors can be approximated appropriately by index options with a semi-nonparametric method. These index options are constructed by efficient algorithms and uniform approximation error under these efficient algorithms are derived. This paper suggests a method to examine state-contingent claims and stochastic discount factors using index options in financial market regardless the market is complete or not.

Suggested Citation

  • Julia Jiang & Weidong Tian, 2019. "Semi-nonparametric approximation and index options," Annals of Finance, Springer, vol. 15(4), pages 563-600, December.
  • Handle: RePEc:kap:annfin:v:15:y:2019:i:4:d:10.1007_s10436-018-0341-4
    DOI: 10.1007/s10436-018-0341-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10436-018-0341-4
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10436-018-0341-4?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. P. Gagliardini & C. Gourieroux & E. Renault, 2011. "Efficient Derivative Pricing by the Extended Method of Moments," Econometrica, Econometric Society, vol. 79(4), pages 1181-1232, July.
    2. Galvani, Valentina & Troitsky, Vladimir G., 2010. "Options and efficiency in spaces of bounded claims," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 616-619, July.
    3. Bansal, Ravi & Viswanathan, S, 1993. "No Arbitrage and Arbitrage Pricing: A New Approach," Journal of Finance, American Finance Association, vol. 48(4), pages 1231-1262, September.
    4. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    5. 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.
    6. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    7. Peter Christoffersen & Steven Heston & Kris Jacobs, 2013. "Capturing Option Anomalies with a Variance-Dependent Pricing Kernel," The Review of Financial Studies, Society for Financial Studies, vol. 26(8), pages 1963-2006.
    8. Hutchinson, James M & Lo, Andrew W & Poggio, Tomaso, 1994. "A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks," Journal of Finance, American Finance Association, vol. 49(3), pages 851-889, July.
    9. Jaroslav Borovička & Lars Peter Hansen & José A. Scheinkman, 2016. "Misspecified Recovery," Journal of Finance, American Finance Association, vol. 71(6), pages 2493-2544, December.
    10. Jérôme Detemple & Yerkin Kitapbayev, 2018. "On American VIX options under the generalized 3/2 and 1/2 models," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 550-581, April.
    11. Steve Ross, 2015. "The Recovery Theorem," Journal of Finance, American Finance Association, vol. 70(2), pages 615-648, April.
    12. David C. Nachman, 1988. "Spanning and Completeness with Options," The Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 311-328.
    13. 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.
    14. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
    15. Nachman, David C., 1987. "Efficient funds for meager asset spaces," Journal of Economic Theory, Elsevier, vol. 43(2), pages 335-347, December.
    16. Duan, Jin-Chuan & Moreau, Arthur F. & Sealey, C. W., 1992. "Spanning with Index Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(2), pages 303-309, June.
    17. Stutzer, Michael, 1996. "A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
    18. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    19. Robert A. Jarrow & Xing Jin & Dilip B. Madan, 1999. "The Second Fundamental Theorem of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 255-273, July.
    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. Shubham Ekapure & Nuruddin Jiruwala & Sohan Patnaik & Indranil SenGupta, 2021. "A data-science-driven short-term analysis of Amazon, Apple, Google, and Microsoft stocks," Papers 2107.14695, arXiv.org.

    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. Tian, Weidong, 2014. "Spanning with indexes," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 111-118.
    2. Almeida, Caio & Freire, Gustavo, 2022. "Pricing of index options in incomplete markets," Journal of Financial Economics, Elsevier, vol. 144(1), pages 174-205.
    3. Barone-Adesi, Giovanni & Fusari, Nicola & Mira, Antonietta & Sala, Carlo, 2020. "Option market trading activity and the estimation of the pricing kernel: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 216(2), pages 430-449.
    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. Jaroslav Borovička & Lars Peter Hansen & José A. Scheinkman, 2016. "Misspecified Recovery," Journal of Finance, American Finance Association, vol. 71(6), pages 2493-2544, December.
    6. Galvani, Valentina, 2007. "A note on spanning with options," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 106-114, July.
    7. Gourieroux, C. & Monfort, A., 2007. "Econometric specification of stochastic discount factor models," Journal of Econometrics, Elsevier, vol. 136(2), pages 509-530, February.
    8. Galvani, Valentina, 2009. "Option spanning with exogenous information structure," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 73-79, January.
    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. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    11. Alexandre M. Baptista, 2005. "Options And Efficiency In Multidate Security Markets," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 569-587, October.
    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. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    14. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    15. Sanjay K. Nawalkha & Xiaoyang Zhuo, 2020. "A Theory of Equivalent Expectation Measures for Contingent Claim Returns," Papers 2006.15312, arXiv.org, revised May 2022.
    16. Dillschneider, Yannick & Maurer, Raimond, 2019. "Functional Ross recovery: Theoretical results and empirical tests," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).
    17. repec:wyi:journl:002108 is not listed on IDEAS
    18. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2015. "Parametric Inference and Dynamic State Recovery From Option Panels," Econometrica, Econometric Society, vol. 83(3), pages 1081-1145, May.
    19. Jensen, Christian Skov & Lando, David & Pedersen, Lasse Heje, 2019. "Generalized recovery," Journal of Financial Economics, Elsevier, vol. 133(1), pages 154-174.
    20. 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.
    21. Tjeerd de Vries, 2021. "A Tale of Two Tails: A Model-free Approach to Estimating Disaster Risk Premia and Testing Asset Pricing Models," Papers 2105.08208, arXiv.org, revised Oct 2023.

    More about this item

    Keywords

    Semi-nonparametric; Index option; Universal approximation error;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • 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:kap:annfin:v:15:y:2019:i:4:d:10.1007_s10436-018-0341-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.