Information-Theoretic Approach to Financial Market Modelling

Battle Count: 84

Highly relevant for quantitative trading and derivative pricing. The MMM provides a parsimonious one-parameter model for pricing and hedging contingent claims using benchmark-neutral pricing. The activity time framework offers a novel way to handle volatility spikes and market microstructure effects. The GOP/benchmark construction is directly applicable to portfolio management. However, the paper is primarily theoretical and does not provide ready-to-implement trading strategies or code. The empirical validation (hedge errors < 0.0001 for zero-coupon bonds) demonstrates practical relevance.

The theoretical framework is mathematically sophisticated (SROU processes, Fokker-Planck equations, Lagrangian optimization, information theory), but the resulting model is remarkably parsimonious with only one parameter. Implementation requires: (1) estimating market time from observable quadratic variation, (2) computing benchmark-neutral prices using SROU process transition densities, (3) constructing the benchmark portfolio. The SROU processes have explicit transition probability densities (noncentral chi-square), facilitating numerical implementation. The main complexity lies in the theoretical derivation rather than practical computation.

The paper is purely theoretical with complete mathematical proofs provided in five appendices. All derivations are self-contained. However, no code, numerical implementations, or datasets are provided. The model requires only one parameter (net risk-adjusted return) and observable market time for pricing/hedging, making it conceptually simple to implement. Empirical validation references prior published work (Platen & Fergusson 2025, Platen & Rendek 2019, etc.).