Lookback options are path-dependent options. In general, the binomial tree methods, as the most popular approaches to pricing options, involve a path dependent variable as well as the underlying asset price for lookback options. However, for floating strike lookback options, a single-state variable binomial tree method can be constructed. This paper is devoted to the convergence analysis of the single-state binomial tree methods both for discretely and continuously monitored American floating strike lookback options. We also investigate some properties of such options, including effects of expiration date, interest rate and dividend yield on options prices, properties of optimal exercise boundaries and so
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