This article empirically analyzes some properties shared by all one-dimensional diffusion option models. Using S&P 500 options, we find that sampled intraday (or interday) call (put) prices often go down (up) even as the underlying price goes up, and 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.

This article provides the economic foundations for valuing derivative securities. In particular, it establishes how the characteristic function (of the future uncertainty) is basis augmenting and spans the payoff universe of most, if not all, derivative assets. From the characteristic function of the state-price density, it is possible to analytically price options on any arbitrary transformation of the underlying uncertainty. By differentiating (or translating) the characteristic function, limitless pricing and/or spanning opportunities can be designed. The strength and versatility of the methodology is inherent when valuing (1) average-interest options, (2) correlation options, and (3) discretely monitored knock-out options.

This article empirically analyzes some properties shared by all one-dimensional diffusion option models. Using S&P 500 options, we find that sampled intraday (or interday) call (put) prices often go down (up) even as the underlying price goes up, and 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.