  The limitations of the classical Black-Scholes model are examined by
comparing calculated and actual historical prices of European call options on
stocks from several sectors of the S&P 500. Persistent differences between the
two prices point to an expanded model proposed by Segal and Segal (1998) in
which information not simultaneously observable or actionable with public
information can be represented by an additional pseudo-Wiener process. A real
linear combination of the original and added processes leads to a commutation
relation analogous to that between a boson field and its canonical momentum in
quantum field theory. The resulting pricing formula for a European call option
replaces the classical volatility with the norm of a complex quantity, whose
imaginary part is shown to compensate for the disparity between prices obtained
from the classical Black-Scholes model and actual prices of the test call
options. This provides market evidence for the influence of a non-classical
process on the price of a security based on non-commuting operators.
