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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.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2008-044.

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Length: 27 pages
Date of creation: Jun 2008
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2008-044

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

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