, 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 … Barle and Cakici (BC). After the formation of IBT we can estimate the implied local volatility and the state price density …

interpreted as volatility, skewness and tail factors.We also find evidence for term structure variation. …

lognormal distributions with constant volatility parameter. In practice volatility changes and the distribution deviates from … allows calculation of future volatility and can be applied to hedging exotic options. -- option pricing ; state price density …

second procedure applies kernel type smoothing in the implied volatility domain. In the conceptually different third approach …