  Refining a discrete model of Cheuk and Vorst we obtain a closed formula for
the price of a European lookback option at any time between emission and
maturity. We derive an asymptotic expansion of the price as the number of
periods tends to infinity, thereby solving a problem posed by Lin and Palmer.
We prove, in particular, that the price in the discrete model tends to the
price in the continuous Black-Scholes model. Our results are based on an
asymptotic expansion of the binomial cumulative distribution function that
improves several recent results in the literature.

Mathematical Finance