CONVERGENCE OF EUROPEAN LOOKBACK OPTIONS WITH FLOATING STRIKE IN THE BINOMIAL MODEL

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

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 04, 1-24

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.

Keywords: Binomial model; lookback; floating strike; Black–Scholes; convergence; asymptotic (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:17:y:2014:i:04:n:s0219024914500253

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DOI: 10.1142/S0219024914500253

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