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Information-Theoretic Approach to Financial Market Modelling

Eckhard Platen

TL;DR

The paper reframes financial markets as information channels and derives a parsimonious minimal market model (MMM) from four information-theoretic assumptions. State variables are scalar stationary diffusions whose normalized factors and growth-optimal portfolio follow squared radial Ornstein-Uhlenbeck processes in market time, with a single governing parameter $\hat{\lambda}$. It shows that surprisal minimization yields gamma stationary densities for normalized factors with dof $d_k=4\omega^k$ and equal factor weights $\omega^k=1/n$, and that information minimization produces a benchmark-time diffusion of dimension four and constant $\hat{\lambda}$, enabling benchmark-neutral pricing via an equivalent BN measure $Q_{S^*}$. Empirically, MMM captures key stylized facts such as stationary volatility, four-degree-of-freedom Student-$t$ log-returns, leverage effects, and rough/3/2 volatility, while producing accurate hedges for inexpensive long-dated bonds and providing a practical, information-theoretic foundation for pricing and hedging in finance.

Abstract

The paper treats the financial market as a communication system, using four information-theoretic assumptions to derive an idealized model with only one parameter. State variables are scalar stationary diffusions. The model minimizes the surprisal of the market and the Kullback-Leibler divergence between the benchmark-neutral pricing measure and the real-world probability measure. The state variables, their sums, and the growth optimal portfolio of the stocks evolve as squared radial Ornstein-Uhlenbeck processes in respective activity times.

Information-Theoretic Approach to Financial Market Modelling

TL;DR

The paper reframes financial markets as information channels and derives a parsimonious minimal market model (MMM) from four information-theoretic assumptions. State variables are scalar stationary diffusions whose normalized factors and growth-optimal portfolio follow squared radial Ornstein-Uhlenbeck processes in market time, with a single governing parameter . It shows that surprisal minimization yields gamma stationary densities for normalized factors with dof and equal factor weights , and that information minimization produces a benchmark-time diffusion of dimension four and constant , enabling benchmark-neutral pricing via an equivalent BN measure . Empirically, MMM captures key stylized facts such as stationary volatility, four-degree-of-freedom Student- log-returns, leverage effects, and rough/3/2 volatility, while producing accurate hedges for inexpensive long-dated bonds and providing a practical, information-theoretic foundation for pricing and hedging in finance.

Abstract

The paper treats the financial market as a communication system, using four information-theoretic assumptions to derive an idealized model with only one parameter. State variables are scalar stationary diffusions. The model minimizes the surprisal of the market and the Kullback-Leibler divergence between the benchmark-neutral pricing measure and the real-world probability measure. The state variables, their sums, and the growth optimal portfolio of the stocks evolve as squared radial Ornstein-Uhlenbeck processes in respective activity times.
Paper Structure (15 sections, 10 theorems, 111 equations, 3 figures)

This paper contains 15 sections, 10 theorems, 111 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Market of Factors
  3. Factors
  4. Benchmark
  5. Numéraire Portfolio
  6. Surprisal-Minimized Market
  7. Normalized Factors
  8. Surprisal Minimization
  9. Benchmark Dynamics
  10. Information-Minimized Market
  11. Benchmark-Neutral Pricing
  12. Information Minimization
  13. Additivity Property of Sums of Independent Factors
  14. Ilustrations
  15. Empirical Evidence

Key Result

Theorem 2.2

For a market of factors and $\tau\in[\tau_{t_0},\infty)$, the sum of the risk premium parameters is conserved and equals the constant $1$, that is, When constructing the benchmark, the vector of weights assigned to the factors corresponds to the vector of risk premium parameters and the benchmark satisfies the SDE for $\tau \in [\tau_{t_0},\infty)$ with $S^*_{\tau_{t_0}}>0$.

Figures (3)

  • Figure 4.1: Logarithms of US savings account denominated MSCI (blue) and EWI114 (red).
  • Figure 4.2: Market time $\tau_t$ (blue) and benchmark time $\tau^*_{\tau_t}$ (red).
  • Figure 4.3: Hedge error for inexpensive zero-coupon bond.

Theorems & Definitions (23)

  • Definition 2.1
  • Theorem 2.2
  • Definition 2.3
  • Theorem 2.4
  • Definition 3.1
  • Definition 3.2
  • Definition 3.3
  • Theorem 3.4
  • Corollary 3.5
  • Theorem 3.6
  • ...and 13 more