Utilizing Parametric and Non-Parametric methods in Black-Scholes Process with Application to Finance

Abstract

In this article, we present that Black-Scholes process is a famous formula in financial mathematics. Our aim is to study the behavior of stochastic parameters in that model with application to Financial Time Stock Exchange FTSE100 Index. We use some parametric (Maximum likelihood, and Unbiased and Efficient) and nonparametric (Penalized least Squares, with different functions for the drift and diffusion coefficients and generally the Black-Scholes process) methods. Moreover, we study the change-point estimation for FTSE100 Index in order to determine these changes, and effects on the behavior of the Black-Scholes process.