Simulation of stochastic processes

Abstract

Simulation of stochastic processes is essential in various fields, including finance. This thesis aims to enhance the comprehension and forecasting of complex models by developing precise simulation methods for stochastic processes, with a specific focus on the application of Euler and Milstein methods. The first part of the thesis establishes the concept of a solution to a Stochastic Differential Equation and delineates the conditions ensuring the existence of a solution. The second part delves into the Euler(-Maruyama) and Milstein methods for approximating solutions to SDEs. Additionally, we provide statements and proofs of convergence for these methods. Furthermore, the last part encompasses the outcomes of numerical experiments.