Pricing discrete Asian barrier options on lattices

Asian barrier options are barrier options whose trigger is based on an average underlying price. They provide the advantages of both Asian options and barrier options. This paper introduces the first quadratic-time lattice algorithm to price European-style Asian barrier options. It is by far the most efficient lattice algorithm with convergence guarantees. The algorithm relies on the Lagrange multipliers to optimally distribute the number of states for each node of the multinomial lattice. We also show experiment results to demonstrate effectiveness and efficiency of our algorithm by comparing with Monte Carlo simulations.