One-state variable binomial models for European-/ American-style geometric Asian options

Abstract

Geometric Asian options are path-dependent options whose payoffs depend on the geometric average of the underlying asset prices. Following Cox et al (1979) arbitrage arguments, We develop one-state variable binomial models for the options on the basis of the idea of Cheuk and Vorst (1997). The models are more efficient and faster than those lattice methods proposed by Hull and White (1993), Ritchken et al (1993), Barraquand and Pudet (1996) and Cho and Lee (1997). We also establish the equivalence of the models and difference schemes.