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Convergence Of European Lookback Options With Floating Strike In The Binomial Model

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  • FABIEN HEUWELYCKX

    (Institut Complexys, Département de Mathématique, Université de Mons, 20 Place du Parc, 7000 Mons, Belgium)

Abstract

In this paper, 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 nonzero. This modelization will also allow us to determine the first term in the expansion of the delta.

Suggested Citation

  • Fabien Heuwelyckx, 2014. "Convergence Of European Lookback Options With Floating Strike In The Binomial Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-24.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:04:n:s0219024914500253
    DOI: 10.1142/S0219024914500253
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    1. Lyuu,Yuh-Dauh, 2002. "Financial Engineering and Computation," Cambridge Books, Cambridge University Press, number 9780521781718, September.
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    Cited by:

    1. Guillaume Leduc & Merima Nurkanovic Hot, 2020. "Joshi’s Split Tree for Option Pricing," Risks, MDPI, vol. 8(3), pages 1-26, August.
    2. Karl Grosse-Erdmann & Fabien Heuwelyckx, 2016. "The pricing of lookback options and binomial approximation," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(1), pages 33-67, April.
    3. Karl Grosse-Erdmann & Fabien Heuwelyckx, 2015. "The pricing of lookback options and binomial approximation," Papers 1502.02819, arXiv.org.
    4. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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