  The stochastic-alpha-beta-rho (SABR) model has been widely adopted in options
trading. In particular, the normal ($\beta=0$) SABR model is a popular model
choice for interest rates because it allows negative asset values. The option
price and delta under the SABR model are typically obtained via asymptotic
implied volatility approximation, but these are often inaccurate and
arbitrageable. Using a recently discovered price transition law, we propose a
Gaussian quadrature integration scheme for price options under the normal SABR
model. The compound Gaussian quadrature sum over only 49 points can calculate a
very accurate price and delta that are arbitrage-free.
