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The concept of Local volatility as well as the Local volatility model are one of the classical topics of mathematical finance.
Although the existing literature is wide, there still exist various problems that have not drawn sufficient attention so far, for example: a) construction of analytical solutions of the Dupire equation for an arbitrary shape of the Local volatility function; b) construction of parametric or non-parametric regression of the Local volatility surface suitable for fast ca.
The concept of Local volatility as well as the Local volatility model are one of the classical topics of mathematical finance
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