Cheuk and Vorst’s method [1996a] can be applied to price barrier options using
one-factor interest rate models when recombining trees are available. For the
Hull-White model, barriers on bonds or swap rates are transformed to time-dependent
barriers on the short rate and we use a time-dependent shift to position the tree
optimally with respect to the barrier. Comparison with barrier options on bonds or
swaps when the observation frequency is discrete confirms that the method is faster
than the Monte Carlo method. Unlike other methods which are only applicable in the
continuously observed case, the lattice methods can be used in both the continuously
and discretely observed cases. We illustrate the methodology by applying it to value
single-barrier swaption and single-barrier bond options. Moreover, we extend Cheuk
and Vorst’s idea [1996b] to double-barrier swaption pricing
