Applications of the Normal Inverse Gaussian (NIG) process in mathematical finance

Many of the papers we have discussed in this lab use L\'{e}vy driven stochastic process rather than the usual Gaussian type. These models are typically complex and empirical results are shown with little detail of how to calibrate and implement the model. The intent here is give the introductory steps required to complete this work. I will show how to incorporate a L\’{e}vy process by modeling, calibrating and pricing European options using a basic NIG process.