Why are BICs better than the prior art?

  BICs are better than the existing pricing or hedging alternatives due to their compelling generality, yet they are computationally tractable.

-With respect to other Basis Instruments alternatives,what about the Arrow-Debreu decomposition

The Arrow Debreu analysis would be good if one were only considering a single future period case. If one tries to extend the concept to a multi-period case, as some authors have done, the complexity of the problem grows exponentially, thereby nullifying its practical use.

-What obout other hedging methods

-What about the Black Scholes delta hedging analysis?

The Black Scholes analysis can be seen as a response to the operational inadequacy of the Arrow Debreu analysis for derivatives pricing and hedging in a multi-period market.

However, it rested on a number of model assumptions that have not been validated in practice. As a result, the derivatives industry has developed a number of alternative models in recent years without clear winner in all circumstances.

-What about Greeks based hedging more generally?

Greeks based hedging methods are often obtained under frictionless markets assumptions which are questionable.

Greeks based hedging depends on a parametric specification of the dynamic of the underlying upon which the derivatives contract to be hedged depend, resulting in a parametric formula for the price of derivatives contracts

It also assumes that the dependence can be approximated by a polynomial of low order (in general order two at most, with the inclusion of "Gamma" terms and various cross differentials)

The cumulation of all those assumptions without a reliable metric for the estimation of the approximation error makes reliance on this approach less than desirable.