Monte Carlo simulation (MCS) is an efficient and flexible method to evaluate financial models and derivative pricing formulas numerically. The first step when valuing derivative instruments via MCS is to discretize the stochastic differential equations (SDE) that govern the dynamics of a given model. The correct and efficient discretization of SDEs is all but trivial and there is a large body of literature that deals with this particular topic. Chapter 10 addresses this topic in detail and introduces a number of correct and approximate discretization schemes for both the index process and the square-root diffusions of the general model framework .
The didactical approach of this book is to illustrate the translation of theoretical models into executable Python scripts. Therefore, the exposition in this chapter only applies one discretization scheme for the index and the other processes, respectively.
Section 12.2 simulates the calibrated model of the previous chapter. Apart from being calibrated, the model now includes the jump component—a topic not addressed in Chapter 10. Section 12.3 then proceeds by valuing European and American options in this set-up by means of MCS.