说明：  This document covers various aspects the Heston model. The structure and topics covered is as follows: Chapter 1 introduces the model and provides theoretical and graphical motivation for its robustness and hence popularity. It also discusses pricing using the Partial Differential Equation and Equivalent Martingale Measure techniques Chapter 2 discusses how the different components of the model can be evaluated computationally and how this can be achieved with different methods. These methods are then compared to each other. Chapter 3 addresses the calibration problem. Different methods are presented as well as practical implementation, results thereof, and comparisons. All the MATLAB code required to implement the model is provided in the appendix