Game of Vols

The absolute values of the spot and strike derivatives of the vanilla option price are probabilities of finishing in the money under different numeraires. At each fixed term, one of these probabilities can be related to the other using a convex distortion function. Using results from convex duality, we show that arbitrage‐free coterminal option prices can always be generated by specifying a convex distortion function. We also propose a parametrization of this convex distortion function and an interpolation method in the time dimension. The option prices generated by this method are free of any arbitrage - the calendar arbitrage, the strike spread arbitrage, and the butterfly spread arbitrage