Lane changes are made frequently on the road and are therefore an important component in analyzing traffic situations. This behavior interferes with surrounding traffic, causes negative shockwaves, and may even lead to collisions. Lane changes can be categorized into mandatory lane changes and discretionary lane changes. There are various factors influencing the decision-making involved in discretionary lane changes, including relative velocity between target and original lane, and lead and lag gaps. The purpose of this paper is to present a stochastic approach for modeling discretionary lane changes with influential factors of velocity and spacing advantages. Using Next Generation Simulation (NGSIM) data, we proposed an exponential probability model with speed difference and lead gap difference between the target lane and the original lane. By transformed linear regression, these traffic variables have actual influences on the lane change probability of discretionary lane changes. The found results can be used for lane change models in microscopic traffic simulation.