Static replications with traffic light options

It is well known that sufficiently regular, one-dimensional payoff functions have an explicit static hedge by bonds, forward contracts, and options in a continuum of strikes. An easy and natural extension of the corresponding representation leads to static hedges based on the same instruments along with traffic light options, which have recently been introduced in the market. It is well known that the second strike derivative of non-discounted prices of vanilla options is related to the risk-neutral density of the underlying asset price in the corresponding absolutely continuous settings. Similar statements hold for traffic light options in sufficiently regular, bivariate settings.