model-free CBOE volatility index (VIX) does not measure market expectation of volatility but that of a linear moment …-combination. Particularly, VIX undervalues (overvalues) volatility when market return is expected to be negatively (positively) skewed …. Alternatively, we develop a model-free generalized volatility index (GVIX). With no diffusion assumption, GVIX is formulated …