This thesis studies a regularization technique of Dupire's formula for Levy jump diffusion models. In particular, a procedure is introduced to reobtain the option prices with a local volatility model. These results are applied to Kou's model, and for that purpose representations of the option price surface and some derivatives are stated. The derived results are then implemented numerically, and the functionality of the introduced procedure is proved using the programming language Matlab. Furthermore issues that arise during this implementation are addressed, such as errors stemming from numerical integration. This work is largely based on the paper How to make Dupire's formula work with jumps by Friz, Gerhold and Yor.