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The pricing of lookback options and binomial approximation. (English) Zbl 1398.91596

Summary: Refining a discrete model of T. H. F. Cheuk and T. C. F. Vorst [“Currency lookback options and observation frequency: a binomial approach”, J. Int. Money Finance 16, 173–187 (1997)], 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.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
62P05 Applications of statistics to actuarial sciences and financial mathematics
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
62E20 Asymptotic distribution theory in statistics
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References:

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