We build a heuristic that takes a given option price in the tails with strike K and extends (for calls, all strikes > K, for put 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 heuristic allows us to scrutinize the volatility surface and test  theories of relative tail option mispricing and overpricing usually built on thin tailed models and modification of the Black-Scholes formula  .
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 ) .
R
heuristic
methodology
R
put
puts
R
alpha
\alpha,
R
heuristic
methodology
A
various
R
mispricing and overpricing
overpricing (
R
modification
minor modifications/fudging
A
)