Calibration of the volatility surface

This thesis consists of two parts, one concerning implied volatility and one concerning local volatility. The SABR model and SVI model are investigated to model implied volatility. The performance of the two models were tested on the Eurcap market in March 2008. Two ways of extracting local volatility are reviewed by a test performed on data from European options based on the S&P 500 index. The first method is a way of solving regularized Dupire’s equation and the other one is based on finding the most likely path.