A convergent quadratic-time lattice algorithm for pricing European-style Asian options

摘要

Asian options are strongly path-dependent derivatives. Although efficient numerical methods and approximate closed-form formulas are available, most lack convergence guarantees. Asian options can also be priced on the lattice. All efficient lattice algorithms keep only a polynomial number of states and use interpolation to compensate for the less than full representation of the states. Let the time to maturity be partitioned into n periods. This paper presents the first O(n2)-time convergent lattice algorithm for pricing European-style Asian options; it is the most efficient lattice algorithm with convergence guarantees. The algorithm relies on the Lagrange multipliers to choose optimally the number of states for each node of the lattice. The algorithm is also memory efficient. Extensive numerical experiments and comparison with existing PDE, analytical, and lattice methods confirm the performance claims and the competitiveness of our algorithm. This result places the problem of European-style Asian option pricing in the same complexity class as that of the vanilla option on the lattice.