Entropic Dynamics of Jump-Diffusion Option Pricing

Battle Count: 76

The paper is highly relevant to quantitative finance and derivatives pricing. It provides a principled derivation of the Merton jump-diffusion model and the Esscher risk-neutral measure, which are directly applicable to option pricing, volatility surface modeling, and risk management. The constraint-modular framework offers a unified approach to model selection. However, the paper is purely theoretical with no empirical validation, no trading strategy, no backtesting, and no implementation guidance. Its relevance is more to quantitative researchers and model developers than to practitioners building trading systems. The implied-volatility smile analysis and jump-risk premium estimation are directly useful for derivatives desks.

The theoretical framework requires understanding of entropic inference, relative entropy, information geometry, and stochastic calculus. The Merton jump-diffusion model itself is well-known and implementable (Poisson-weighted sum of Black-Scholes prices). The novel contribution is the derivation methodology rather than a new computational algorithm. Implementing the pricing formula (Eq. 57) requires numerical summation over Poisson-weighted Black-Scholes branches and solving a transcendental equation for the Esscher multiplier theta. The Kolmogorov-Feller PIDE (Eq. 71) requires numerical methods (finite differences, FFT, or Monte Carlo) for general payoff structures. The entropic inference framework itself is not computationally implemented in the paper.

The paper provides complete analytical derivations with all equations, constraints, and proofs laid out in detail (including Appendices A-C for the Poisson count derivation, Kolmogorov-Feller equation derivation, and mean log-return calculation). However, there is no code, no numerical examples, no parameter calibration, and no empirical validation. The framework is purely theoretical and mathematical, making it reproducible in principle but not in a computational sense. The methodology is fully specified through the constraint structure and MaxEnt procedure.