W.W. Hsu and Y.-D. Lyuu (Taiwan)
: Option pricing, binomial model, path dependent derivative, Asian option, complexity
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 avail able, 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 lat tice algorithm runs in 2O( 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 polyno mial 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(n2.5 ) time. This paper presents an O(n2 )-time convergent lattice algorithm for pricing European-style fixed-strike Asian op tions. The algorithm is the most efficient yet published in the literature with convergence guarantees. It is also mem ory efficient; for example, it can work with n as high as 3, 000 without any difficulties. Extensive numerical exper iments 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.
Important Links:
Go Back
