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Convergence of European Lookback Options with Floating Strike in the Binomial Model

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  • Fabien Heuwelyckx

Abstract

In this article we study the convergence of a European lookback option with floating strike evaluated with the binomial model of Cox-Ross-Rubinstein to its evaluation with the Black-Scholes model. We do the same for its delta. We confirm that these convergences are of order 1/Sqrt(n). For this, we use the binomial model of Cheuk-Vorst which allows us to write the price of the option using a double sum. Based on an improvement of a lemma of Lin-Palmer, we are able to give the precise value of the term in 1/Sqrt(n) in the expansion of the error; we also obtain the value of the term in 1/n if the risk free interest rate is non zero. This modelisation will also allow us to determine the first term in the expansion of the delta.

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  • Fabien Heuwelyckx, 2013. "Convergence of European Lookback Options with Floating Strike in the Binomial Model," Papers 1302.2312, arXiv.org, revised Oct 2013.
    • Handle: RePEc:arx:papers:1302.2312
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    1. Goldman, M Barry & Sosin, Howard B & Gatto, Mary Ann, 1979. "Path Dependent Options: "Buy at the Low, Sell at the High"," Journal of Finance, American Finance Association, vol. 34(5), pages 1111-1127, December.
    2. Lo-Bin Chang & Ken Palmer, 2007. "Smooth convergence in the binomial model," Finance and Stochastics, Springer, vol. 11(1), pages 91-105, January.
    3. Babbs, Simon, 2000. "Binomial valuation of lookback options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1499-1525, October.
    4. Francine Diener & MARC Diener, 2004. "Asymptotics of the price oscillations of a European call option in a tree model," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 271-293, April.
    5. Cheuk, Terry H. F. & Vorst, Ton C. F., 1997. "Currency lookback options and observation frequency: A binomial approach," Journal of International Money and Finance, Elsevier, vol. 16(2), pages 173-187, April.
    6. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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