CONTINUOUS TIME PROCESSES IN TIMES OF CRISIS: THE CASE OF GBM AND CEV MODELS

Abstract: This research aims at studying continuous time models within different stock market environments. We assume that the modeling of continuous time processes may be altered whether an equity market is experiencing a crisis or a pre-crisis period. As a benchmark index, the S&P500 has been chosen for this study and the sampling periods in question include the Black Monday of 1987, the Dot-Com of 2001, and the more recent 2007 Financial Crisis. Among the continuous time processes family, this study covers the Geometric Brownian Motion (GBM) and the Constant Elasticity of Variance (CEV). After estimating and analyzing their respective parameters using the Maximum Likelihood Estimation method, both the Jarque-Bera normality test and the Likelihood Ratio are performed on the two models. Unlike most research that support the use of CEV over GBM, this research test outcomes show that there is no strong argument that could favor the addition of a discount factor i.e. CEV over the Black-Scholes based process, the GBM model.