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 Time
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abstract
The formulation of quantum mechanics within the framework of entropic dynamics includes several new elements. In this paper we concentrate on one of them: the implications for the theory of time. Entropic time is introduced as a book-keeping device to keep track of the accumulation of changes. One new feature is that, unlike other concepts of time appearing in the so-called fundamental laws of physics, entropic time incorporates a natural distinction between past and future.
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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.