Local volatility recovery from call prices
= Local volatility recovery from call prices
{title2=$\sigma^2=2(C_T+rKC_K)/(K^2C_{KK})$}
Where $C_{KK}>0$, rearranging the <Dupire equation> gives $\sigma(T,K)^2=2(C_T+rKC_K)/(K^2C_{KK})$. The strike curvature represents discounted density, while the adjusted maturity derivative gives the local diffusion contribution.