SOME FORMULAE FOR A NEW TYPE OF PATH-DEPENDENT OPTION

被引：41

作者：

Akahori, Jiro ^{[1
]}

机构：

[1] Univ Tokyo, Dept Math Sci, Tokyo 113, Japan

来源：

ANNALS OF APPLIED PROBABILITY | 1995年 / 5卷 / 02期

关键词：

Options; Black-Scholes model; Feynman-Kac formula; arc-sine law; percentiles;

D O I：

10.1214/aoap/1177004769

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we present an explicit form of the distribution function of the occupation time of a Brownian motion with a constant drift (if there is no drift, this is the well-known arc-sine law). We also define the alpha-percentile of the stock price and give an explicit form of the distribution function of this random variable. Using this explicit distribution, we calculate the price of a new type of path-dependent option, called the alpha-percentile option. This option was first introduced by Miura and is based on order statistics.

引用

页码：383 / 388

页数：6

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