, especially on the BS implied volatility. Implied binomialtrees (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 thestate price density …

option prices. But some of its assumptions, like constant volatility or log-normal distribution of asset prices,do not find … implied volatility surface. To overcome this problem Carr and Madan (1999) developed a fast method to compute option prices …

three market regimes. Aconsistent parametric framework of stochastic volatility is used. All empiricalmarket utility …

convenience yields for CO2 emission allowance futures. We conduct an empirical study on price behavior, volatility term structure … high fraction of the yields can be explained by the price level and volatility of the spot prices. We conclude that the …