quant research // summarizing the paperLOADING
Mohammad Abedi · 2026-07-07
The paper shows that well-known option-pricing models don't need to be assumed outright — they can be derived from basic information/entropy principles plus a few stated constraints. By choosing log-price as the key variable and splitting price moves into a smooth channel and a sudden-jump channel, the authors recover the Merton jump-diffusion model (and Black-Scholes when jumps are removed). The same reasoning also selects the Esscher transform for pricing in incomplete markets and reproduces the implied volatility smile.
Why it matters: It offers a unifying, principled way to understand why standard option models take the form they do, and clarifies that jumps are what generate the volatility smile that flat Black-Scholes misses. For anyone modeling options, it reinforces which information (jump frequency and jump-size moments) actually drives smile behavior and pricing-measure choice.
⚠ This is a theoretical derivation that reframes existing models rather than providing new empirical results or a tested trading edge.
Standard models of stock price dynamics and option valuation usually begin by postulating stochastic processes. This paper develops an entropic inference framework that derives these processes from information constraints. The key symmetry is that markets reward returns rather than price levels, which selects log price as the dynamical variable. Price changes are represented by two channels. The continuous channel carries constraints of continuity and directionality. The jump channel carries the arrival rate and the first two moments of jump size. Since these constraints apply to disjoint parts of the microstate, the channels factorize. The resulting dynamics is the Merton jump diffusion, with Geometric Brownian Motion as the no jump limit. The log price density satisfies the Kolmogorov Feller equation, whose no jump limit is the Fokker Planck equation. The same inferential principle, with no arbitrage imposed through the mean log return, selects the Esscher transform from the many martingale measures available in an incomplete market. The option price then satisfies Mertons partial integro differential equation, and the risk neutral mixture of lognormal distributions generates the implied volatility smile. The Black Scholes results are recovered when jumps vanish. What changes from one model to another is not the inference, but the information supplied to it.
Go deeper: a full research-committee breakdown of this paper, its assumptions and failure modes, and how its method would apply to a specific ticker or your watchlist. See StockTools AI →
AI summary generated from the paper’s public abstract via arXiv; it may miss nuance — read the source before relying on it. Thank you to arXiv for its open-access interoperability; StockTools is not affiliated with arXiv, and all rights remain with the authors. Educational only, not financial advice.