Mispricing of Index Options with Respect to Stochastic Dominance Bounds? A Reply

Constantinides and Perrakis (2002, 2007) derive a lower bound on the price of an option such that an investor increases her utility by buying the option at the ask price if the ask price is lower than the lower bound; and by writing the option at the bid price if the bid price is higher than upper bound. Contrary to the evidence in Constantinides et al. (2009, 2011) who demonstrate several violations of mainly the upper bound on call prices and document a tradable anomaly by exploiting this mispricing, Wallmeier (2020) claims that practically all options on the S&P 500, Eurostoxx 50, and DAX indices lie within the bounds. The main reason for the discrepancy is that Wallmeier erroneously inflates the volatility input to the bounds by about 2% by using the at-the-money implied volatility which is approximately the risk-neutral volatility instead of the physical volatility, as required by the model.