A JUMP-DIFFUSION WITH STOCHASTIC VOLATILITY AND INTEREST RATE

In this study, we present the application of Time Changed Levy method to model a jump-diffusion process with stochastic volatility and stochastic interest rate. We apply the Lewis Fourier transform method as well as the risk neutral expectation pricing method to derive a formula for a European option pricing. These combining methods give quite a short route to derive the formula and make it efficient to compute option prices. We also show the calibration of our model to the real market with global and local optimization algorithms.