# Dupire Formula question

I want to calculate the local volatility from Dupire's formula:

$$\sigma _{VL}^{2} (K,T,S_{0}) = \frac{\frac{\partial C}{\partial T}}{\frac{1}{2} K^{2} \frac{\partial^2 C}{\partial K^2}}$$

So I use the aproximation forms as :

$$\frac{\partial C }{\partial T} \cong \frac{C(K, T + \Delta T) - C(K,T - \Delta T}{2 \Delta t}$$

$$\frac{\partial^2 C}{\partial K^2} \cong \frac{C(K- \Delta K, T) - 2C(K,T) + C(K + \Delta K,T )}{(\Delta K)^{2}}$$

With this date to get the local volatility of the option SPX(288.5,April 15), should I do this?:

$$\frac{\partial C }{\partial T} \cong \frac{2.02 - 1.51}{2 * 3}$$

$$\frac{\partial^2 C}{\partial K^2} \cong \frac{2.03 -2*1.65 + 1.4}{0.5^2}$$

• I have same problem as you faced. I just wanted to know were you able to solve this issue. If yes can you please share your feedback and let me know if you have practically implemented something with real data. Thanks