SABR Calibration

Although local volatility models are self-consistent, arbitrage-free and can be calibrated to match observed market skews and smiles, it has been observed that the dynamic behaviour of smiles and skews predicted by local volatility models contradicts the one observed in the marketplace.

A stochastic volatility model, called the SABR model, is derived to solve this problem. The SABR model is a parameterized pricing model for European options. To use the model properly, it must be calibrated to market skews and smiles.