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

被引：5

作者：

Heuwelyckx, Fabien ^{[1
]}

机构：

[1] Univ Mons, Inst Complexys, Dept Math, B-7000 Mons, Belgium

来源：

INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE | 2014年 / 17卷 / 04期

关键词：

Binomial model; lookback; floating strike; Black-Scholes; convergence; asymptotic;

D O I：

10.1142/S0219024914500253

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

摘要：

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/root 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/root 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.

引用

页数：24

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