In this paper, we show how transformation techniques coupled with a convolution integral
can be used to solve a generalised option-pricing model, including the Black–Scholes model.
Such equations are parabolic and the special convolutions are extremely involved as they arise
from an initial value problem. New symmetries are derived to obtain solutions through an
application of the invariant surface condition. The main outcome is that the point symmetries
are effective in producing exact solutions that satisfy a given initial condition, such as those
represented by a call-option.
