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In his article, Dupire (1994) developed the local volatility approach under the assumption that options are traded for a continuum of maturities and strikes. In reality, only a finite number of options generating a grid of strikes and maturities is traded. Then the reconstruction of the local volatility function is obtained by interpolation methods. However,...


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Yes looks like ATM volatility. It’s forward (he also calls it forward forward volatility). Say you have the volatility of an option with 30 days maturity, $\sigma_1$ and $T_1$; and the volatility of an option with 60 days maturity, $\sigma_2$ and $T_2$.The 0-30 bucket will have $\sigma_1$ , whereas the 30-60 days bucket will have the forward volatility ...


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