Parametric arbitrage-free models for implied smile dynamics

Based on the theory of Tangent Levy model [1] developed by R. Carmona and S. Nadtochiy, this thesis gives a paramatrized realization of dynamic implied smile.\ud \ud After specifying a Dirac style Levy measure, we give argument about the consistency issue of our model with the Tangent Levy Model. A corresponding no arbitrage drift condition is derived for the parameters. Numerical setup under our model for option pricing and parameter estimation for calibration is given. Implementation results are illustrated in detail and in the end we provide with simulation results of one day ahead implied smile