Building the gap
Gapped tail insurance would be built upon so-called barrier options, derivatives that either begin or cease to exist if an asset reaches a certain price level. Instead of buying, say, a six-month Dow Jones Industrial Average (DJIA) vanilla 9000 put, you could buy a 9000 put that knocks-out at 8000 and a 9000 put that knocks-in at 7000.
If during those six months the DJIA never reaches 8000 (near 30% drop from early January 2011’s levels) you would have owned a 9000 put throughout. If the DJIA does reach 8000 but doesn’t reach 7000 (near 40% drop), you would end up unhedged (the put would be knocked-out). If 7000 is reached, you again become the owner of the 9000 put (the put is knocked-in). In other words, your protection would be akin to a vanilla put except if the market stays below 8000 and above 7000 (the gap region). You are insured from disaster (a dive to 8000) and from mega disaster (a dive below 7000), though not from a well-defined semi-mega-disaster.
How much would you save by valiantly going exotic? Given early January 2011’s levels for stocks and interest rates and using a rough Black-Scholes model, the combo of exotic DJIA 9000 puts could be roughly 55% (with 25% volatility), 45% (with 30% volatility) or 35% (35% volatility) cheaper than the vanilla alternative. Those are tasty savings.
Whether you should go this route depends on your probability assessments. If you believe that if the market sinks 30%, then it would surely spiral into the abyss of -40% returns, then the combo would have provided protection for a market gone to hell far more affordably than a straight put. But what if the market decides to rest in the purgatory of 8000-7000 (see "Finding a spot to avoid")?
While the knock-out/knock-in combo surely appears as good value from an initial premium point of view, it is essential to point out that it may suffer from much more turbulent market value than the simpler vanilla alternative. Barrier options can experience wild swings in mark-to-market valuation, a phenomenon typically described as having discontinuous Greeks.