  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.
