This chapter brie
y summarizes basic concepts of stochastic calculus,
using intuitive examples. First, the fundamentals of probability spaces are intro-
duced by working with a simple example of a stochastic process. Next, stochastic
processes are introduced in connection with a natural ltration and a martingale.
Then, we introduce a stochastic integral and Ito's formula, which is an important
tool for solving stochastic differential equations. Finally, we address some funda-
mental examples of stochastic differential equations, which simply model the price
process of a nancial asset.
Although these subjects are applied in practice to interest rate modeling, the
denitions are given for the one-dimensional case for the sake of simplicity. We
complement this with some basic results for multi-dimensional cases in Section
2.7, at the end of this chapter.