IDEAS home Printed from https://ideas.repec.org/p/wyi/wpaper/001991.html
   My bibliography  Save this paper

Revealing the Implied Risk-neutral MGF with the Wavelet Method

Author

Listed:
  • Emmanuel Haven
  • Xiaoquan Liu
  • Chenghu Ma
  • Liya Shen

Abstract

Options are believed to contain unique information about the risk- neutral moment generating function (MGF hereafter) or the risk-neutral probability density function (PDF hereafter). This paper applies the wavelet method to approximate the risk-neutral MGF of the under- lying asset from option prices. Monte Carlo simulation experiments are performed to elaborate how the risk-neutral MGF can be obtained using the wavelet method. The Black-Scholes model is chosen as the benchmark model. We offer a novel method for obtaining the implied risk-neutral MGF for pricing out-of-sample options and other complex or illiquid derivative claims on the underlying asset using information obtained from simulated data.

Suggested Citation

  • Emmanuel Haven & Xiaoquan Liu & Chenghu Ma & Liya Shen, 2013. "Revealing the Implied Risk-neutral MGF with the Wavelet Method," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    • Handle: RePEc:wyi:wpaper:001991
    as

    Download full text from publisher

    File URL: https://econpub.xmu.edu.cn/research/repec/upload/200711121642157055475115776.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Davidson, Russell & Labys, Walter C & Lesourd, Jean-Baptiste, 1998. "Wavelet Analysis of Commodity Price Behavior," Computational Economics, Springer;Society for Computational Economics, vol. 11(1-2), pages 103-128, April.
    2. 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.
    3. Yousefi, Shahriar & Weinreich, Ilona & Reinarz, Dominik, 2005. "Wavelet-based prediction of oil prices," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 265-275.
    4. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    5. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    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. 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.
    8. Connor Jeff & Rossiter Rosemary, 2005. "Wavelet Transforms and Commodity Prices," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(1), pages 1-22, March.
    9. Antoniou, Antonios & Vorlow, Constantinos E., 2005. "Price clustering and discreteness: is there chaos behind the noise?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 389-403.
    10. 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.
    11. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    12. repec:bla:jfinan:v:53:y:1998:i:2:p:499-547 is not listed on IDEAS
    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. Haven, Emmanuel & Liu, Xiaoquan & Ma, Chenghu & Shen, Liya, 2009. "Revealing the implied risk-neutral MGF from options: The wavelet method," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 692-709, March.
    2. repec:wyi:journl:002097 is not listed on IDEAS
    3. repec:wyi:journl:002092 is not listed on IDEAS
    4. 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.
    5. repec:wyi:journl:002108 is not listed on IDEAS
    6. Abarca Gustavo & Rangel José Gonzalo & Benavides Guillermo, 2010. "Exchange Rate Market Expectations and Central Bank Policy: The case of the Mexican Peso-US Dollar from 2005-2009," Working Papers 2010-17, Banco de México.
    7. 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.
    8. Marian Micu, 2005. "Extracting expectations from currency option prices: a comparison of methods," Computing in Economics and Finance 2005 226, Society for Computational Economics.
    9. Äijö, Janne, 2008. "Impact of US and UK macroeconomic news announcements on the return distribution implied by FTSE-100 index options," International Review of Financial Analysis, Elsevier, vol. 17(2), pages 242-258.
    10. Monteiro, Ana Margarida & Tutuncu, Reha H. & Vicente, Luis N., 2008. "Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity," European Journal of Operational Research, Elsevier, vol. 187(2), pages 525-542, June.
    11. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    12. Jondeau, Eric & Rockinger, Michael, 2000. "Reading the smile: the message conveyed by methods which infer risk neutral densities," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 885-915, December.
    13. Patrick Dennis & Stewart Mayhew, 2009. "Microstructural biases in empirical tests of option pricing models," Review of Derivatives Research, Springer, vol. 12(3), pages 169-191, October.
    14. Haven, Emmanuel & Liu, Xiaoquan & Shen, Liya, 2012. "De-noising option prices with the wavelet method," European Journal of Operational Research, Elsevier, vol. 222(1), pages 104-112.
    15. Neuhaus, Holger, 1995. "The information content of derivatives for monetary policy: Implied volatilities and probabilities," Discussion Paper Series 1: Economic Studies 1995,03e, Deutsche Bundesbank.
    16. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
    17. Liu, Xiaoquan & Cao, Yi & Ma, Chenghu & Shen, Liya, 2019. "Wavelet-based option pricing: An empirical study," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1132-1142.
    18. 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.
    19. Duca, Ioana Andreea & Ruxanda, Gheorghe, 2013. "A View on the Risk-Neutral Density Forecasting of the Dax30 Returns," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 101-114, June.
    20. Almeida, Caio & Freire, Gustavo, 2022. "Pricing of index options in incomplete markets," Journal of Financial Economics, Elsevier, vol. 144(1), pages 174-205.
    21. Jondeau, E. & Rockinger, M., 1998. "Reading the Smile: The Message Conveyed by Methods Which Infer Risk Neutral," Working papers 47, Banque de France.
    22. Don M. Chance & Thomas A. Hanson & Weiping Li & Jayaram Muthuswamy, 2017. "A bias in the volatility smile," Review of Derivatives Research, Springer, vol. 20(1), pages 47-90, April.
    23. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.

    More about this item

    Keywords

    Implied risk-neutral MGF; wavelets; options; Black-Scholes model.;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wyi:wpaper:001991. 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: WISE Technical Team (email available below). General contact details of provider: https://www.wise.xmu.edu.cn/english/ .

    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.