volatility and long-term trend are driven by an external stochastic factor process. The robust utility functional is defined in …

, 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 …

Implied volatility is one of the key issues in modern quantitative finance, since plain vanilla option prices contain … yield low dimensional representations of the implied volatility surface (IVS). We discussestimation issues of the model and …

implied volatilities (IV) plays an important role, since volatility is the crucial parameter in the Black-Scholes (BS) pricing … known as volatility smiles or smirks that contradict the assumption of constant volatility in the BS pricing model. On the …

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 …

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 …