  In this article, we show how the scaling symmetry of the SABR model can be
utilized to efficiently price European options. For special kinds of payoffs,
the complexity of the problem is reduced by one dimension. For more generic
payoffs, instead of solving the 1+2 dimensional SABR PDE, it is sufficient to
solve $N_V$ uncoupled 1+1 dimensional PDE's, where $N_V$ is the number of
points used to discretize one dimension. Furthermore, the symmetry argument
enables us to obtain prices of multiple options, whose payoffs are related to
each other by convolutions, by valuing one of them. The results of the method
are compared with the Monte Carlo simulation.
