Reasonable evaluation of VIX options for the Taiwan stock index

Abstract

This study aims to reasonably evaluate VXO (volatility index option) prices on the Taiwan stock index using four popular pricing models, namely, Black-Scholes (BS), square root (SQR), log-normal Ornstein-Uhlenbeck (LOU), and GARCH models. Since VXOs have not been traded yet in Taiwan options market, we directly employ the physical probability measure to evaluate the VXOs. This study examined the Taiwan and CBOE VIX data from December 2006 to January 2018 and found that the estimated option prices generally appear in the descending order as GARCH > BS > SQR > LOU. That is, when VIX has heteroscedasticity, the BS model could undervalue the VXOs. Additionally, when VIX has no mean-reverting property, the SQR and LOU models could seriously undervalue the VXOs, especially for the long-term maturity options. While existing studies have not sufficiently evaluated the Taiwan VXOs, the results of this study can provide future reference for investors and securities companies when evaluating the Taiwan VXOs.