  We build a methodology that takes a given option price in the tails with
strike $K$ and extends (for calls, all strikes > $K$, for puts all strikes $<
K$) assuming the continuation falls into what we define as "Karamata Constant"
over which the strong Pareto law holds. The heuristic produces relative prices
for options, with for sole parameter the tail index $\alpha$, under some mild
arbitrage constraints.
  Usual restrictions such as finiteness of variance are not required.
  The methodology allows us to scrutinize the volatility surface and test
various theories of relative tail option overpricing (usually built on thin
tailed models and minor modifications/fudging of the Black-Scholes formula).
