The authors show that maximum-entropy reasoning, together with a scale-invariance argument for log returns, yields the standard Garman-Kohlhagen foreign-exchange option pricing model.
Geometry from Information Geometry
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abstract
We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe the full geometry of space but only its conformal geometry -- the geometry up to local changes of scale. Remarkably, this is precisely what is needed to model "physical" space in general relativity.
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Entropic Dynamics of Exchange Rates and Options
The authors show that maximum-entropy reasoning, together with a scale-invariance argument for log returns, yields the standard Garman-Kohlhagen foreign-exchange option pricing model.