Foundations of Mathematical Finance and Stochastic Calculus

Abstract

This chapter presents the necessary foundations to understand the mathematical, financial and computational aspects behind this model. In the first section we start with simple interest rate necessities and go on to financial Derivatives which are necessary to understand to correctly calibrate and use the model for pricing. The section 2.2 starts with the most important aspects in stochastic calculus which is the key step to understand and work with stochastic differential equations. One additional topic in this section is the no-arbitrage Pricing which are a prerequisite to understand modern option pricing theory. The final section in this chapter gives the reader an overview about the computational aspects which are important to build this model.