What question did this study set out to answer?

Formulate an entropic-inference framework that systematically derives stock-price stochastic dynamics and option valuation formulas directly from encoded information rather than postulating them a priori.

August 16, 2026EntropyOpen Access

Entropic Dynamics of Jump-Diffusion Option Pricing

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MAMohammad Abedi

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Overview

Theoretical analysis derives Merton jump-diffusion dynamics using an entropic-inference framework, indicating that option pricing models emerge directly from specified informational constraints.

Key Points

Formulate an entropic-inference framework that systematically derives stock-price stochastic dynamics and option valuation formulas directly from encoded information rather than postulating them a priori.
Applied entropic inference constrained by return symmetry to establish log-price as the fundamental dynamical variable.
Separated price evolution into disjoint continuous channels (continuity and directionality) and jump channels (arrival rate and jump-size moments).
Enforced no-arbitrage conditions via mean log-returns to derive risk-neutral martingale measures in an incomplete market.
Proved that independent continuous and jump microstate constraints factorize into the Merton jump-diffusion process, governing log-price density through the Kolmogorov–Feller equation.
Derived the Esscher transform directly from informational constraints, yielding Merton’s partial integro-differential equation for option premiums.
Generated the implied-volatility smile from a risk-neutral mixture of lognormals, recovering standard Black–Scholes and Fokker–Planck equations when jump processes vanish.

Cite This Study

Mohammad Abedi (2026) studied this question.

synapsesocial.com/papers/6a81791ff2fb91fc834ac44e https://doi.org/10.3390/e28080914

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August 16, 2026EntropyOpen Access

Entropic Dynamics of Jump-Diffusion Option Pricing

View Full Paper

Ask AI

Bookmark

Authors

MAMohammad Abedi

Discussion

Member takes

Overview

Theoretical analysis derives Merton jump-diffusion dynamics using an entropic-inference framework, indicating that option pricing models emerge directly from specified informational constraints.

Key Points

Formulate an entropic-inference framework that systematically derives stock-price stochastic dynamics and option valuation formulas directly from encoded information rather than postulating them a priori.
Applied entropic inference constrained by return symmetry to establish log-price as the fundamental dynamical variable.
Separated price evolution into disjoint continuous channels (continuity and directionality) and jump channels (arrival rate and jump-size moments).
Enforced no-arbitrage conditions via mean log-returns to derive risk-neutral martingale measures in an incomplete market.
Proved that independent continuous and jump microstate constraints factorize into the Merton jump-diffusion process, governing log-price density through the Kolmogorov–Feller equation.
Derived the Esscher transform directly from informational constraints, yielding Merton’s partial integro-differential equation for option premiums.
Generated the implied-volatility smile from a risk-neutral mixture of lognormals, recovering standard Black–Scholes and Fokker–Planck equations when jump processes vanish.

Cite This Study

Mohammad Abedi (2026) studied this question.

synapsesocial.com/papers/6a81791ff2fb91fc834ac44e https://doi.org/10.3390/e28080914

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