Financial Relativity: An Information-Geometric Interpretation of Asset Pricing

Battle Count: 74

The paper provides a novel theoretical lens for understanding asset pricing, volatility dynamics, and risk premia. The endogenous volatility relation (Σ_t ∝ π_t(1-π_t)) offers a testable prediction for event-driven trading. The geometric interpretation of risk premia as apparent drift from reference frame mismatch could inform factor investing and hedging strategies. However, the framework is highly abstract and not yet operationalized into concrete trading signals or backtestable strategies. Its primary value is conceptual reframing rather than direct algorithmic implementation.

The theoretical framework requires advanced mathematics including Hilbert space theory, stochastic differential equations, filtering theory, differential geometry, and information theory. The discrete numerical example is tractable, but implementing the continuous financial field equation and posterior geometry evolution for real markets would require significant computational infrastructure. The challenge lies in empirically identifying structural sources, estimating posterior geometries from market data, and calibrating the coupling parameter κ. The framework is extensible but not yet packaged as a practical tool.

The paper is primarily theoretical with a numerical illustration (Section 4) using a 3-period, 8-state finite-state model. No empirical data analysis is conducted. The mathematical derivations are self-contained with proofs in appendices. However, the framework is conceptual and lacks a complete computational implementation or empirical validation pipeline. Reproducing the numerical example is straightforward, but applying the framework to real market data requires significant additional modeling choices.