  Economic and financial theories and practice essentially deal with uncertain
future. Humans encounter uncertainty in different kinds of activity, from
sensory-motor control to dynamics in financial markets, what has been subject
of extensive studies. Representation of uncertainty with normal or lognormal
distribution is a common feature of many of those studies. For example,
proposed Bayessian integration of Gaussian multisensory input in the brain or
log-normal distribution of future asset price in renowned Black-Scholes-Merton
(BSM) model for pricing contingent claims.
  Standard deviation of log(future asset price) scaled by square root of time
in the BSM model is called implied volatility. Actually, log(future asset
price) is not normally distributed and traders account for that to avoid
losses. Nevertheless the BSM formula derived under the assumption of constant
volatility remains a major uniform framework for pricing options in financial
markets. I propose that one of the reasons for such a high popularity of the
BSM formula could be its ability to translate uncertainty measured with implied
volatility into price in a way that is compatible with human intuition for
measuring uncertainty.
  The present study deals with mathematical relationship between uncertainty
and the BSM implied volatility. Examples for a number of common probability
distributions are presented. Overall, this work proposes that representation of
various probability distributions in terms of the BSM implied volatility
profile may be meaningful in both biological and financial worlds. Necessary
background from financial mathematics is provided in the text.
