Efficient Pricing Options with Barrier and Lookback Features Under Levy Processes

We derive a general formula for pricing options with barrier and/or lookback features, which covers several types of options studied in the literature and new types of options, and demonstrate that the pricing formula can be efficiently realized using the methodology developed in Kudryavtsev and Levendorskii (Finance Stoch.13: 531-562, 2009). As one of examples, we consider a new type of barrier-lookback options, which expire if the barrier is reached or crossed before maturity, and pay the same amount as standard lookback options otherwise. We demonstrate advantages of our approach in terms of accuracy and convergence