Superposed Ornstein-Uhlenbeck Processes

Auteurs : Julius Esunge University of Mary Washington and Auguste Muhau, Universite Nouveaux Horizons
Resume :  In this work we present and define the superposed Ornstein-
Uhlenbeck processes by following the Barndorff-Nielsen approach. The Black-
Scholes model is the most referenced model in financial mathematics, but due
to its limitations, particularly its constant volatility, the Black-Scholes model
fails to capture the nature of the data in finance. In order to overcome this
limitation, we present the Barndorff-Nielsen and Shephard model with, as a
volatility model, the superposed Ornstein-Uhlenbeck processes which is sum
of independent Ornstein-Uhlenbeck processes driven by Lévy process. In
order to show that a financial model with constant volatility is less reliable in
finance than one with stochastic process as a volatility, we will simulate the
trajectories of the Black-Scholes model and that of the Barndorff-Nielsen and
Shephard model and show that the Barndorff-Nielsen and Shephard model
provides a better fit than the Black-Scholes model.4. MOts cles : Superposed Ornstein-Uhlenbeck processes, Barndorff-Nielsen and
Shephard model, Black-Scholes-Merton model, Ornstein-Uhlenbeck driven by Lévy process5. Lien : https://digitalcommons.lsu.edu/josa/vol1/iss2/6/