Numerics of implied binomial trees

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 649 Discussion Paper ; No. 2008,044

Classification and Topics

• Classification: Wirtschaft ; Asset Pricing; Trading Volume; Bond Interest Rates ; Contingent Pricing; Futures Pricing; option pricing ; Estimation: General
• Subject: Implied tree models ; implied olatility ; local volatility ; option pricing ; Optionspreistheorie ; Volatilität ; Entscheidungsbaum ; Statistische Verteilung ; Numerisches Verfahren ; Theorie ; Schätzung ; EU-Staaten

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Härdle, Wolfgang Karl ; Myšičková, Alena
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (where): Berlin
• (when): 2008

Further information

• Handle: http://hdl.handle.net/10419/25284
• Last update: 10.03.2025, 11:42 AM CET