ORAKULUM: An Information-Impact Asset Pricing Model Introducing a Jump-Diffusion Framework for Information-Driven Markets

Standard asset pricing models treat price dynamics as a stochastic process driven by undifferentiated random noise, rendering them agnostic about the primary engine of price discovery: the arrival of economically significant information. This paper introduces ORAKULUM, a structured Information-Impact Asset Pricing Model that reconceptualises the log-price as a signed information ledger. Each market-relevant event appends a weighted entry that either permanently revises the market consensus or temporarily disturbs it before decaying exponentially toward the new equilibrium. Mathematically, ORAKULUM is a jump-diffusion process combining a Wiener component for continuous micro-uncertainty with a Poisson-driven jump component for discrete macroeconomic and geopolitical shocks. The log-price identity xt=x0+μ·t+∑Ai+∑Bi·e(−γt−ti)+σ·W(t) decomposes price dynamics into permanent and transient information impact, admits a natural event catalogue calibration, and supports Monte Carlo scenario simulation. We present the complete theoretical foundations, a closed-form expected path solution, a gradient-descent calibration procedure, and a fully documented Python3 reference implementation. An empirical illustration applies the model to XAU/USD and EUR/USD market data downloaded from Yahoo Finance, demonstrating ORAKULUM’s capacity to generate economically interpretable, real-time prediction clouds in response to central bank communications, inflation releases, and geopolitical shocks.