Rejoinder to a remark on Lin and Chang's paper ‘Consistent modeling of S&P 500 and VIX derivatives’

We appreciate the thorough review and very useful comments of Cheng, Ibraimi, Leippold, and Zhang. The suggestions have helped significantly to improve our original approximation formula and lead us to provide an exact solution under the Lin and Chang (2010) framework and we thank the editor to give us an illustration chance. This rejoinder has two parts. The first presents a VIX option pricing formula in the stochastic volatility (SV) model. The numerical results using the authors' framework and notations are illustrated, too. The second is to explain our approximate formula in Lin and Chang (2010) and points out the limitation and calibrating technique of the approximation.