A CONVERGENT QUADRATIC-TIME LATTICE ALGORITHM FOR PRICING EUROPEAN-STYLE ASIAN OPTIONS

摘要

Asian options are popular path-dependent derivatives. However, how to price them efficiently and accurately is a long-standing problem. Although efficient numerical methods and approximate closed-form formulas are available, most lack convergence guarantees. Asian options can also be priced on the lattice. Suppose the time to maturity is partitioned into n periods. The best exact convergent lattice algorithm runs in 2{sup}O({the square root of}n) time. (An exact algorithm is one which does not employ approximations beyond the discretization of the continuous-time model.) All efficient lattice algorithms that are not exact keep only a polynomial number of states and use interpolation to compensate for the less than full representation of the states. The best such algorithm before the current paper runs in O(n{sup}2.5) time. This paper presents an O(n{sup}2)-time convergent lattice algorithm for pricing European-style fixed-strike Asian options. The algorithm is the most efficient yet published in the literature with convergence guarantees. It is also memory efficient; for example, it can work with n as high as 3, 000 without any difficulties. Extensive numerical experiments and comparison with existing methods confirm the performance claims. This result places the European-style Asian option pricing problem in the same complexity class as that of the vanilla option.