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Numerics of Implied Binomial Trees

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  • Wolfgang Härdle
  • Alena Mysickova

Abstract

Market option prices in last 20 years con rmed deviations from the Black and Scholes (BS) models assumptions, especially on the BS implied volatility. Implied binomial trees (IBT) models capture the variations of the implied volatility known as \volatility smile". They provide a discrete approximation to the continuous risk neutral process for the underlying assets. In this paper, we describe the numerical construction of IBTs by Derman and Kani (DK) and an alternative method by Barle and Cakici (BC). After the formation of IBT we can estimate the implied local volatility and the state price density (SPD). We compare the SPD estimated by the IBT methods with a conditional density computed from a simulated di usion process. In addition, we apply the IBT to EUREX option prices and compare the estimated SPDs. Both IBT methods coincide well with the estimation from the simulated process, though the BC method shows smaller deviations in case of high interest rate, particularly.

Suggested Citation

  • Wolfgang Härdle & Alena Mysickova, 2008. "Numerics of Implied Binomial Trees," SFB 649 Discussion Papers SFB649DP2008-044, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2008-044
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    References listed on IDEAS

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    1. Pierre Cahuc & André Zylberberg, 2004. "Labor Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 026203316x, January.
    2. repec:eee:labchp:v:2:y:1986:i:c:p:1139-1181 is not listed on IDEAS
    3. Froot, Kenneth A., 1989. "Consistent Covariance Matrix Estimation with Cross-Sectional Dependence and Heteroskedasticity in Financial Data," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(03), pages 333-355, September.
    4. Rick L. Williams, 2000. "A Note on Robust Variance Estimation for Cluster-Correlated Data," Biometrics, The International Biometric Society, vol. 56(2), pages 645-646, June.
    5. José Mata & José A. F. Machado, 2005. "Counterfactual decomposition of changes in wage distributions using quantile regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 445-465.
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    More about this item

    Keywords

    Implied Tree Models; Implied Volatility; Local Volatility; Option Pricing;

    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
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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