Abstract: Why are we interested in calibrating a local volatility surface? It is mostly to price dependent exotic options which are not very liquid and the proper market quotes are not available. Local volatility also gives rise to some interesting relative value trading strategies. There are a number of local volatility calibration methods available, but no one agrees on the “perfect” calibration method. There is no single correct answer. Perhaps that is the reason why calibration is not only a science but also an art. The problem of calibration requires creativity and that is the reason why there is no perfect calibration model. There is always room for improvement in these kinds of problems.