This paper shows how one can obtain a continuous-time preference-free option pricing model with a path-dependent volatility as the limit of a discrete-time GARCH model. In particular, the continuous-time model is the limit of a discrete-time GARCH model of Heston and Nandi (1997) that allows...

This paper improves continuous-time variance swap approximation formulas to derive exact returns on benchmark VIX option portfolios. The new methodology preserves the variance swap interpretation that decomposes returns into realized variance and option implied-variance.We apply this new...