We propose a model‐independent method to account for the early exercise premiums in American options on non‐dividend paying stocks. We find that our estimates of early exercise premium are generally larger than the estimates by existing methods. Given the American options on the Exchange‐Traded Funds (ETFs) of gold, silver, natural gas, and crude oil, we find strong empirical evidence of variance risk premiums for these commodities, over a volatility term structure up to 18 months. Furthermore, we show that volatility indexes constructed by using existing methods tend to overestimate the risk‐neutral variance, and consequently the magnitude of variance risk premium. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:452–472, 2017