  A new mathematical model for the Black-Scholes equation is proposed to
forecast option prices. This model includes new interval for the price of the
underlying stock as well as new initial and boundary conditions. Conventional
notions of maturity time and strike prices are not used. The Black-Scholes
equation is solved as a parabolic equation with the reversed time, which is an
ill-posed problem. Thus, a regularization method is used to solve it. This idea
is verified on real market data for twenty liquid options. A trading strategy
is proposed. This strategy indicates that our method is profitable on at least
those twenty options. We conjecture that our method might lead to significant
profits of those financial institutions which trade large amounts of options.
We caution, however, that detailed further studies are necessary to verify this
conjecture.
