The paper examines the valuation of European- and American-style volatility options based on a general equilibrium stochastic volatility framework. The volatility models can be summarized by a risk neutralized process taking the form \[ dV_{t}=V{t}[(r-{\delta}_{t}^{V}) dt+ {\sigma}_{t}^{V} dZ_{t}^{*}] \] for appropriate choices of the coefficients \(({\delta}^V,{\sigma}^V)\). Here \({\delta}^V\) can be interpreted as an implicit ``dividend'' rate on the underlying volatility. The starting point is a general class of volatility processes which are known to be viable, namely, the geometric Brownian motion and the mean-reverting processes such as Gaussian, square-root and log processes. The structure of the exercise set and the valuation of American volatility options for a general volatility process are discussed. Explicit valuation formulas for European and American options are then provided for each of the four models mentioned above. A unified derivation of some of the components of these option values are presented. This unified derivation relies on the explicit formula for the truncated characteristic function of the normal distribution which is the common building block underlying each of the four volatility models. Unlike American options, European call options on volatility are found to display concavity at high levels of volatility.