This paper introduces a novel arterial blood pressure (ABP) signal model that generates statistically accurate synthetic signals with known characteristics. Using parameter identification from real ABP signals to form base parameter templates, our model applies stochastic processes to modulate cardiac cycle period and shape. A real-time control component modulates model parameters between cycle boundaries to emulate properties of real cardiovascular signals, such as arrhythmia, ectopic beats, resonances in the heart-rate variability spectrum, and respiratory cycle modulation of ABP signal amplitude. We present several examples to illustrate the capability of the proposed model.