IDEAS home Printed from https://ideas.repec.org/p/fip/fedawp/96-5.html
   My bibliography  Save this paper

Estimation of risk-neutral and statistical densities by Hermite polynomial approximation: with an application to Eurodollar futures options

Author

Listed:
  • Peter A. Abken
  • Dilip B. Madan
  • Buddhavarapu Sailesh Ramamurtie

Abstract

This paper expands and tests the approach of Madan and Milne (1994) for pricing contingent claims as elements of a separable Hilbert space. We specialize the Hilbert space basis to the family of Hermite polynomials and use the model to price options on Eurodollar futures. Restrictions on the prices of Hermite polynomial risk for contingent claims with different times to maturity are derived. These restrictions are rejected by our empirical tests of a four-parameter model. The unrestricted results indicate skewness and excess kurtosis in the implied risk-neutral density. These characteristics of the density are also mirrored in the statistical density estimated from a time series on LIBOR. The out-of-sample performance of the four-parameter model is consistently better than that of a two-parameter version of the model.

Suggested Citation

  • Peter A. Abken & Dilip B. Madan & Buddhavarapu Sailesh Ramamurtie, 1996. "Estimation of risk-neutral and statistical densities by Hermite polynomial approximation: with an application to Eurodollar futures options," FRB Atlanta Working Paper 96-5, Federal Reserve Bank of Atlanta.
  • Handle: RePEc:fip:fedawp:96-5
    as

    Download full text from publisher

    File URL: https://www.atlantafed.org/-/media/documents/research/publications/wp/1996/wp965.pdf
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Clement, E. & Gourieroux, C. & Monfort, A., 2000. "Econometric specification of the risk neutral valuation model," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 117-143.
    2. Eric Benhamou & Alexandre Duguet, 2000. "A 2 Dimensional Pde For Discrete Asian Options," Computing in Economics and Finance 2000 33, Society for Computational Economics.
    3. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    4. 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.
    5. Lu, Junwen & Qu, Zhongjun, 2021. "Sieve estimation of option-implied state price density," Journal of Econometrics, Elsevier, vol. 224(1), pages 88-112.
    6. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance 0207008, University Library of Munich, Germany.
    7. Gatfaoui, Hayette, 2015. "Pricing the (European) option to switch between two energy sources: An application to crude oil and natural gas," Energy Policy, Elsevier, vol. 87(C), pages 270-283.
    8. Benhamou, Eric & Duguet, Alexandre, 2003. "Small dimension PDE for discrete Asian options," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11), pages 2095-2114.
    9. Coutant, Sophie & Jondeau, Eric & Rockinger, Michael, 2001. "Reading PIBOR futures options smiles: The 1997 snap election," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 1957-1987, November.
    10. Ruijun Bu & Kaddour Hadri, 2005. "Estimating the Risk Neutral Probability Density Functions Natural Spline versus Hypergeometric Approach Using European Style Options," Working Papers 200510, University of Liverpool, Department of Economics.
    11. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "American options with stochastic dividends and volatility: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 53-92.
    12. René Lalonde, 1999. "The Information Content of Interest Rate Futures Options," Staff Working Papers 99-15, Bank of Canada.
    13. Capelle-Blancard, G. & Jurczenko, E., 1999. "Une application de la formule de Jarrow et Rudd aux options sur indice CAC 40," Papiers d'Economie Mathématique et Applications 2000.05, Université Panthéon-Sorbonne (Paris 1).
    14. Steven L. Heston & Alberto G. Rossi, 2017. "A Spanning Series Approach to Options," The Review of Asset Pricing Studies, Oxford University Press, vol. 7(1), pages 2-42.
    15. 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.
    16. Robert R Bliss & Nikolaos Panigirtzoglou, 2000. "Testing the stability of implied probability density functions," Bank of England working papers 114, Bank of England.
    17. Marian Micu, 2005. "Extracting expectations from currency option prices: a comparison of methods," Computing in Economics and Finance 2005 226, Society for Computational Economics.
    18. Darolles, Serge & Laurent, Jean-Paul, 2000. "Approximating payoffs and pricing formulas," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1721-1746, October.
    19. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
    20. Ramaprasad Bhar & Carl Chiarella, 2000. "Expectations of monetary policy in Australia implied by the probability distribution of interest rate derivatives," The European Journal of Finance, Taylor & Francis Journals, vol. 6(2), pages 113-125.
    21. Nessim Souissi, 2017. "The Implied Risk Neutral Density Dynamics: Evidence from the S&P TSX 60 Index," Journal of Applied Mathematics, Hindawi, vol. 2017, pages 1-10, June.
    22. Arturo Leccadito & Pietro Toscano & Radu S. Tunaru, 2012. "Hermite Binomial Trees: A Novel Technique For Derivatives Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-36.
    23. Peter A. Abken & Saikat Nandi, 1996. "Options and volatility," Economic Review, Federal Reserve Bank of Atlanta, vol. 81(Dec), pages 21-35.
    24. Steven L. Heston & Alberto G. Rossi, 2017. "A Spanning Series Approach to Options," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 7(1), pages 2-42.
    25. 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.

    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:fip:fedawp:96-5. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Rob Sarwark (email available below). General contact details of provider: https://edirc.repec.org/data/frbatus.html .

    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.