Psychological barriers are prevalent among various asset classes, and it is important to consider their impact on the prices of derivative securities. This paper demonstrates the potential existence of such barriers on the S&P 500 Index and examines their impact on this index's rate of return and volatility. It focuses on deriving analytic European option prices under the assumption that the dynamics of stock prices follow a threshold model; this paper also evaluates this model's empirical performance relative to the Black–Scholes and constant elasticity of variance (CEV) models. The in-sample calibration result of the threshold model is found to be superior. Furthermore, it is found that the model provides an efficient hedging method in terms of dollar-value hedging errors. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 35:52–74, 2015