In this talk, we investigate the number of state variables required for options pricing and the dynamic features that govern the evolution of these state variables. We adopt a nonparametric regression technique with the use of model-free implied variance-swap prices of various maturities as proxies for the transformed state variables. The methodology is applied to the prices of S&P500 index options during the period 1996-2005. We find that, in addition to the index value itself, two state variables, approximated by a short-term variance-swap price and a long-term variance-swap price, are adequate for pricing the index options and fitting the data well in time-series and cross-sections. The drift and the squared diffusion of the state variables exhibit strong non-linearity, which explains why popular models in the literature are unable to fit the data satisfactorily.