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Numerics of implied binomial trees

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  • Härdle, Wolfgang Karl
  • Myšičková, Alena

Abstract

Market option prices in last 20 years confirmed 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 difusion 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

  • Härdle, Wolfgang Karl & Myšičková, Alena, 2008. "Numerics of implied binomial trees," SFB 649 Discussion Papers 2008-044, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2008-044
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    Cited by:

    1. Jansen, Jeroen & Das, Sanjiv R. & Fabozzi, Frank J., 2018. "Local volatility and the recovery rate of credit default swaps," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 1-29.

    More about this item

    Keywords

    Implied tree models; implied olatility; local volatility; option pricing;
    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
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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