  This paper presents a novel way to predict options price for one day in
advance, utilizing the method of Quasi-Reversibility for solving the
Black-Scholes equation. The Black-Scholes equation solved forwards in time with
Tikhonov regularization as an ill-posed problem allows for extrapolation of
option prices. This provides high-accuracy results, which can be further
improved by applying Neural Network Machine Learning to the solution of the
Black-Scholes equation as well as initial and boundary conditions and implied
volatility. Using historical option and stock price data the results obtained
from the method of Quasi-Reversibility and Machine Learning method are compared
in terms of accuracy, precision and recall. It is shown that these methods can
be applied to the real-world trading within a variety of trading strategies.
