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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
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    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. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance 0207008, EconWPA.
    6. Benhamou, Eric & Duguet, Alexandre, 2003. "Small dimension PDE for discrete Asian options," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11-12), pages 2095-2114, September.
    7. 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.
    8. Ruijun Bu & Kaddour Hadri, 2005. "Estimating the Risk Neutral Probability Density Functions Natural Spline versus Hypergeometric Approach Using European Style Options," Research Papers 200510, University of Liverpool Management School.
    9. 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.
    10. Mc Manus, Des, 1999. "The Information Content of Interest Rate Futures Options," Staff Working Papers 99-15, Bank of Canada.
    11. 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.
    12. repec:oup:rapstu:v:7:y:2017:i:1:p:2-42. is not listed on IDEAS
    13. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, Elsevier.
    14. Robert R Bliss & Nikolaos Panigirtzoglou, 2000. "Testing the stability of implied probability density functions," Bank of England working papers 114, Bank of England.
    15. Marian Micu, 2005. "Extracting expectations from currency option prices: a comparison of methods," Computing in Economics and Finance 2005 226, Society for Computational Economics.
    16. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
    17. 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.
    18. 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.
    19. Peter A. Abken & Saikat Nandi, 1996. "Options and volatility," Economic Review, Federal Reserve Bank of Atlanta, issue Dec, pages 21-35.
    20. repec:oup:rasset:v:7:y:2017:i:1:p:2-42. is not listed on IDEAS
    21. 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.
    22. 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.

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