Foreign exchange option symmetry based on domestic-foreign payoff invariance

We introduce and study a general symmetry relationship in a foreign exchange market. Conceptually our paper is based on (Kholodnyi, 1995) which, to the best of our knowledge, introduced for the first time to finance such fundamental notions from modern theoretical physics as observables, invariant or coordinate-free descriptions of a phenomenon, symmetries and related group-theoretical methods. We state our results rather formally from the mathematical standpoint omitting rigorous proofs and supporting them whenever possible with appropriate financial justification.