Convergence of Binomial Tree Method for European/American Path-Dependent Options

The binomial tree method, first proposed by Cox et al. (1979), is the most popular approach to pricing options. By introducing an additional path-dependent variable, such method can be readily extended to the valuation of path-dependent options. Barraquand et al. (1996) presented the so-called forward shooting grid method, which is a modification of binomial tree method, to cope with arithmetic average options. In this paper, using numerical analysis and the notion of viscosity solutions, we present a unifying theoretical framework to show the uniform convergence of binomial tree methods for European/American path-dependent options, including arithmetic average options, geometric average options and lookback options