The Merton jump-diffusion process, the Esscher transform, and the implied volatility smile are derived from Maximum Entropy inference applied to log-price dynamics with continuity, directionality, and jump constraints.
Entropic Dynamics: Mechanics without Mechanism
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abstract
Entropic Dynamics is a framework in which dynamical laws such as those that arise in physics are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to constraints reflecting the information that is relevant to the problem at hand. In this work I review the derivation of quantum theory but the fact that Entropic Dynamics is based on inference methods that are of universal applicability suggests that it may be possible to adapt these methods to fields other than physics.
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Entropic Dynamics of Jump-Diffusion Option Pricing
The Merton jump-diffusion process, the Esscher transform, and the implied volatility smile are derived from Maximum Entropy inference applied to log-price dynamics with continuity, directionality, and jump constraints.