Computation of first-order Greeks for barrier options using chain rules   for Wiener path integrals
  This paper presents a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian type and with time-dependent trigger levels. In particular, we develop chain rules for Wiener path integrals between two curves that arise in the computation of first-order Greeks for barrier options. We also illustrate the effectiveness of our method through numerical examples. 
Kensuke Ishitani
q-fin.MF