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... bedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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 diffusion 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. For about 20 years now, discrepancies between market option prices and Black and Scholes (BS) prices have widened. The observed market option price showed that the BS implied volatility, computed from the market option price by inverting the BS formula varies with strike price and time to expiration. These variations are known as "the volatility smile (skew)" and volatility term structure, respectively.