Is there an informationally passive benchmark for option pricing incorporating maturity?

Figlewski proposed testing the incremental contribution of the Black-Scholes model by comparing its performance against an “informationally passive” benchmark, which was defined to be an option pricing formula satisfying static no-arbitrage constraints. In this paper we extend Figlewski's analysis to include options of more than one maturity. Once maturity has been included in the model, any “informationally passive” call pricing function is consistent with some “active” model. In this sense, the notion of a passive model cannot be extended to pricing formulas incorporating option maturity. We derive the index dynamics of the active model implicit in Figlewski's implied G example. These dynamics are far more complicated than the dynamics of the Samuelson-Black-Scholes or Bachelier models. The main implication of our analysis is that an appropriate benchmark for assessing option pricing models should in fact have simple dynamics, such as those of Bachelier or the Black-Scholes models. This is despite the fact that the maturity extension of Figlewski's model gives as good a fit as the Black-Scholes model.