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Open AccessArticle

Entropic Dynamics of Exchange Rates and Options

Department of Physics, University at Albany-SUNY, Albany, NY 12222, USA
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Entropy 2019, 21(6), 586; https://doi.org/10.3390/e21060586
Received: 27 April 2019 / Revised: 4 June 2019 / Accepted: 6 June 2019 / Published: 13 June 2019
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. View Full-Text
Keywords: entropic inference; maximum entropy; entropic dynamics; Fokker–Planck equation; Garman–Kohlhagen model; Black–Scholes–Merton partial differential equation entropic inference; maximum entropy; entropic dynamics; Fokker–Planck equation; Garman–Kohlhagen model; Black–Scholes–Merton partial differential equation
MDPI and ACS Style

Abedi, M.; Bartolomeo, D. Entropic Dynamics of Exchange Rates and Options. Entropy 2019, 21, 586.

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