  We demonstrate effectiveness of the first-order algorithm from [Milstein,
Tretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier
option pricing. The algorithm uses the weak Euler approximation far from
barriers and a special construction motivated by linear interpolation of the
price near barriers. It is easy to implement and is universal: it can be
applied to various structures of the contracts including derivatives on
multi-asset correlated underlyings and can deal with various type of barriers.
In contrast to the Brownian bridge techniques currently commonly used for
pricing barrier options, the algorithm tested here does not require knowledge
of trigger probabilities nor their estimates. We illustrate this algorithm via
pricing a barrier caplet, barrier trigger swap and barrier swaption.
