The Dupire equation is well-known and mentioned in thousands of articles. Although I could not find a lot of documentation about a consistent and proper way of implementing the formula (The difficulty is mainly estimating correctly the derivatives).
The question I want to raised is especially how to estimate properly the derivatives used in this formula.
For instance I have derived a grid of option prices for different strikes and expiries. The grid is supposed to be very dense with more than 200 prices for a given expiry. Lets say the grid is consistent and does not admit any arbitrages. My understanding is estimating derivatives with respect to T and K by using central finite difference scheme, with a bump of epsilon of the forward/expiry:
1. Estimate the derivative of option with respect to T by a bump of T 2. Estimate the second order derivative with respect to K 3. Apply the Dupire formula.
Are there any methods of derivative calculation to develop a full and consistent local volatility pricer?