An estimation method is developed for extracting the latent stochastic volatility from VIX, a volatility index for the S&P 500 index return produced by the Chicago Board Options Exchange (CBOE) using the so-called model-free volatility construction. Our model specification encompasses all mean-reverting stochastic volatility option pricing models with a constant-elasticity of variance and those allowing for price jumps under stochastic volatility. Our approach is made possible by linking the latent volatility to the VIX index via a new theoretical relationship under the risk-neutral measure. Because option prices are not directly used in estimation, we can avoid the computational burden associated with option valuation for stochastic volatility/jump option pricing models. Our empirical findings are: (1) incorporating a jump risk factor is critically important; (2) the jump and volatility risks are priced; (3) the popular square-root stochastic volatility process is a poor model specification irrespective of allowing for price jumps or not. Our simulation study shows that statistical inference is reliable and not materially affected by the approximation used in the VIX index construction.
