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

Efficient valuation method for the SABR model