# Tag Info

One does not estimate the local volatility at a given $T$ and $K$. Instead, Dupire's formula actually gives $\sigma(T,K)$ for all $T$ and $K$. $$\sigma^2(t_0,S_0;T,K)= \frac{\frac{\partial C}{\partial T} + (r - q)K \frac{\partial C}{\partial K} + qC}{\frac{1}{2} K^2 \frac{\partial^2C}{\partial K^2}}$$ where $C(t_0,S_0;T,K)$ are the call prices for ...