Abstract:

            Stochastic differential equations (SDEs) have become standard models for financial quantities such as asset prices, interest rates, and their derivatives. To give an example from financial mathematics, the classical model for a stock price is that of a geometric Brownian motion. In this paper, an introduction to the theory of stochastic differential equations (SDE) is given and have shown how this theory can be useful in financial modeling. The following main topics are included: concept of Brownian motion, stochastic integrals, its formula, stochastic differential equations, applications to the Black-Scholes model. The aim is to solve a particular financial problem, namely that of finding the correct price of a European call option.

Keywords: Brownian motion, Stochastic differential equations, Ito integral, Black-scholes model