Numerics of Implied Binomial Trees

Wolfgang Karl Härdle and Alena Myšičková

No SFB649DP2008-044, SFB 649 Discussion Papers from Humboldt University, Collaborative Research Center 649

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 diusion 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.

Keywords: Implied Tree Models; Implied Volatility; Local Volatility; Option Pricing (search for similar items in EconPapers)
JEL-codes: G12 G13 C13 (search for similar items in EconPapers)
Date: 2008-06

Downloads: (external link)
http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2008-044.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:hum:wpaper:sfb649dp2008-044

Access Statistics for this paper

More papers in SFB 649 Discussion Papers from Humboldt University, Collaborative Research Center 649
Contact information at EDIRC.
Series data maintained by Janine Tellinger ().