Financial Probabilities from Fisher Information

TL;DR

This paper introduces a new method combining Fisher information with asset pricing to reconstruct implicit probability densities from security prices, offering a smoother alternative to maximum entropy methods.

Contribution

It develops a practical Fisher information-based approach for inverse problems in asset pricing, transforming density estimation into solving a differential equation.

Findings

Fisher information yields smoother probability densities than maximum entropy.

The method effectively reconstructs densities from bond and option prices.

Numerical solutions are feasible with existing differential equation techniques.

Abstract

We present a novel synthesis of Fisher information and asset pricing theory that yields a practical method for reconstructing the probability density implicit in security prices. The Fisher information approach to these inverse problems transforms the search for a probability density into the solution of a differential equation for which a substantial collection of numerical methods exist. We illustrate the potential of this approach by calculating the probability density implicit in both bond and option prices. Comparing the results of this approach with those obtained using maximum entropy we find that Fisher information usually results in probability densities that are smoother than those obtained using maximum entropy.