  The Hull-White one factor model is used to price interest rate options. The
parameters of the model are often calibrated to simple liquid instruments, in
particular European swaptions. It is therefore very important to have very
efficient pricing formula for simple instruments. Such a formula is proposed
here for European swaption. Based on a very efficient corrector type
approximation the approximation is efficient both in term of precision and in
term of spped. In our implementation the approximation is more than ten time
faster than the direct pricing formula and more than twenty time faster than
the Jamshidian trick.
