Parameter estimation in a Black–Scholes model using mixed methods

Abstract

his paper addresses the problem of parameter estimation in the Black–Scholes model. Our objective is to estimate the unknown parameters of the underlying stochastic differential equation (Geometric Brownian motion) based on discrete-time observation data. To improve estimation accuracy, we propose here an improvement to the application of the first-passage time method, known for the reliability of its estimation results. However, in practice, the data often follow ascending or descending trajectories, which makes its application challenging. To address this issue, we use the indirect inference method, which provides a suitable solution to the problem