The Stochastic Alpha Beta Rho (SABR) is a popular stochastic volatility model for pricing interest rate derivatives. In contrast to local volatility models, the SABR model correctly captures the movement of the volatility smile. The model's density can be approximated by the solution of a one-dimensional partial differential equation (pde). Solving for the density using the Crank-Nicolson discretisation results in loss of accuracy in computation of European option prices. This paper proposes a non-oscillatory scheme for approximating the density function using an exponential time integration scheme. The non-oscillatory property leads to an efficient scheme for option valuation via quadrature of the density function. Numerical examples illustrate that European option prices can be computed with high accuracy.