Do Call Prices and the Underlying Stock Always Move in the Same Direction?

This article empirically analyzes some properties shared by all one-dimensional diffusion option models. Using Samp;P 500 options, we find that when sampled intraday (or inter-day), (i) call (put) prices often go down (up) even as the underlying price goes up, and (ii) call and put prices often increase, or decrease, together. Our results are valid after controlling for time-decay and market microstructure effects. Therefore, one-dimensional diffusion option models cannot be completely consistent with observed option-price dynamics; options are not redundant securities, nor ideal hedging instruments---puts and the underlying asset prices may go down together