Financial Relativity: An Information-Geometric Interpretation of Asset Pricing

TL;DR

This paper introduces Financial Relativity, an information-geometric framework that unifies asset pricing concepts by interpreting risk-neutral and physical measures as geometric structures shaped by informational constraints.

Contribution

It proposes a novel geometric approach to asset pricing, reinterpreting probability measures and price dynamics within a unified information geometry framework.

Findings

Risk-neutral measure viewed as a posterior probability geometry.

Asset prices as geometric projections of terminal payoffs.

Endogenous volatility arises from posterior uncertainty.

Abstract

Classical asset pricing relies on the risk-neutral measure $Q$ for valuation, yet its economic interpretation is typically anchored in a physical measure $P$. This creates an inherent asymmetry: pricing is governed by $Q$, while meaning resides in $P$, making it difficult to provide a unified account of asset pricing within a single conceptual framework. This paper proposes an alternative perspective based on information geometry, termed Financial Relativity. Its central principle is the relativity of probabilistic reference frames: $P$ and $Q$ have no intrinsic hierarchy, but instead represent geometric structures induced by different informational constraints. Terminal structural information shapes probability geometry, which in turn governs how information is expressed in prices. Within this framework, the risk-neutral measure is reinterpreted as a posterior probability geometry. Asset prices are characterized as geometric projections of terminal payoffs onto information subspaces, and their dynamics reflect the progressive manifestation of structural information under evolving geometry. We develop both discrete and continuous financial field equations to describe the formation of probability geometry and derive geodesic price dynamics in which volatility arises endogenously from posterior uncertainty. The framework provides a unified explanation for price fluctuations, event-driven behavior, and risk premia, and yields testable implications, including structural links between volatility and posterior variance and measures of price informational efficiency. By integrating structural information, probability measures, and price dynamics within a single geometric framework, the paper offers a coherent, extensible, and empirically tractable reinterpretation of asset pricing.