Rate of convergence of trinomial formula to Black–Scholes formula

Pub Date : 2024-06-01 DOI:10.1016/j.spl.2024.110167

Yuttana Ratibenyakool , Kritsana Neammanee

引用次数: 0

Abstract

The Black–Scholes formula which was introduced by three economists, Black et al. (1973) has been widely used to calculate the theoretical price of the European call option. In 1979, Cox, Ross and Rubinstein (Cox et al., 1979) gave the binomial formula which is a tool to find the price of European option and showed that this formula converges to the Black–Scholes formula as the number of periods $(n)$ converges to infinity. In 1988, Boyle investigated another formula that is used to find the price of European option, that is the trinomial formula. In 2015, Puspita et al. gave examples to show that the trinomial formula is closed to the Black–Scholes formula. After that, Ratibenyakool and Neammanee (2020) gave the rigorous proof of this convergence. In this paper, we show that the rate of convergence is of order $\frac{1}{\sqrt{n}}$ .

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三项式公式与布莱克-斯科尔斯公式的收敛速度

Black 等人（1973 年）提出的 Black-Scholes 公式被广泛用于计算欧式看涨期权的理论价格。1979 年，Cox、Ross 和 Rubinstein（Cox et al.，1979 年）给出了二项式公式，这是一种计算欧式期权价格的工具，并表明当期数（n）趋近于无穷大时，该公式与 Black-Scholes 公式趋同。1988 年，Boyle 研究了另一个用于计算欧式期权价格的公式，即三项式公式。2015 年，Puspita 等人举例说明了三项式公式与 Black-Scholes 公式是封闭的。之后，Ratibenyakool 和 Neammanee（2020 年）给出了这种收敛性的严格证明。在本文中，我们证明了收敛速率为 1n 阶。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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