TITLE:
Brownian Motion & the Stochastic Behavior of Stocks
AUTHORS:
Pantelis Tassopoulos, Yorgos Protonotarios
KEYWORDS:
Brownian Motion, Stochastic Calculus, Stochastic Differential Equation, Stocks, Itô Integral
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.12 No.1,
February
15,
2022
ABSTRACT: In this paper, we test the effectiveness of predicting the behavior of stocks utilizing stochastic calculus. We begin by exploring the intuition of Brownian motion by explaining its birth through the observations of Robert Brown and later through Bachelier’s work on its applications to the financial market and finally its rigorous and concretized form proposed by Norbert Wiener. The aforementioned motivates a stochastic differential equation to model the future price fluctuations of a stock wherein It? integration is prominent and consequently expanded upon. The final part of this paper focuses on the accuracy of the model by back testing it with Apple stock and deriving a correlation coefficient.