Option pricing utilizing a jump diffusion model with a log mixture normal jump distribution

In this thesis, we present a formula for pricing European options using a jump diffusion process. We are explicitly defining the distribution of the jumps as a log mixture of normal random variables. In order to do so, we first determine the distribution for a mixture of normal random variables and the log mixture of normals. We use QQ-plots to show that this distribution could effectively be used to model realized market returns. The EM Algorithm is implemented to determine the parameters for our jump diffusion model. An analytic formula for option pricing is derived in this thesis. The EM Algorithm and the formulas we derive are used to provide examples.