  An Entropic Dynamics of exchange rates is laid down to model the dynamics of
foreign exchange rates, FX, and European Options on FX. The main objective is
to represent an alternative framework to model dynamics. Entropic inference is
an inductive inference framework equipped with proper tools to handle
situations where incomplete information is available. Entropic Dynamics is an
application of entropic inference, which is equipped with the entropic notion
of time to model dynamics. The scale invariance is a symmetry of the dynamics
of exchange rates, which is manifested in our formalism. To make the formalism
manifestly invariant under this symmetry, we arrive at choosing the logarithm
of the exchange rate as the proper variable to model. By taking into account
the relevant information about the exchange rates, we derive the Geometric
Brownian Motion, GBM, of the exchange rate, which is manifestly invariant under
the scale transformation. Securities should be valued such that there is no
arbitrage opportunity. To this end, we derive a risk-neutral measure to value
European Options on FX. The resulting model is the celebrated Garman-Kohlhagen
model.

Pricing of Securities