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May, 1995 Some Formulae for a New Type of Path-Dependent Option
Jiro Akahori
Ann. Appl. Probab. 5(2): 383-388 (May, 1995). DOI: 10.1214/aoap/1177004769

Abstract

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.

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Jiro Akahori. "Some Formulae for a New Type of Path-Dependent Option." Ann. Appl. Probab. 5 (2) 383 - 388, May, 1995. https://doi.org/10.1214/aoap/1177004769

Information

Published: May, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0834.90026
MathSciNet: MR1336874
Digital Object Identifier: 10.1214/aoap/1177004769

Subjects:
Primary: 90A69
Secondary: 60G44 , 60H30

Keywords: arc-sine law , Black-Scholes model , Feynman-Kac formula , Options , percentiles

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 2 • May, 1995
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