JOINT DISTRIBUTION OF A SPECTRALLY NEGATIVE LEVY PROCESS AND ITS OCCUPATION TIME, WITH STEP OPTION PRICING IN VIEW

被引：16

作者：

Guerin, Helene ^{[1
]}

Renaud, Jean-Francois ^{[2
]}

机构：

[1] Univ Rennes 1, IRMAR, Campus Beaulieu, F-35042 Rennes, France

[2] Univ Quebec Montreal UQAM, Dept Math, 201 Av President Kennedy, Montreal, PQ H2X 3Y7, Canada

来源：

ADVANCES IN APPLIED PROBABILITY | 2016年 / 48卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Occupation time; spectrally negative Levy process; fluctuation theory; scale function; step option; 1ST PASSAGE TIMES;

D O I：

10.1017/apr.2015.17

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：

We study the distribution E-x[exp (-q integral(t)(0) 1((a, b))(X-s) ds); X-t epsilon dy], where -infinity <= a < b < infinity, and where q, t > 0 and x epsilon R for a spectrally negative Levy process X. More precisely, we identify the Laplace transform with respect to t of this measure in terms of the scale functions of the underlying process. Our results are then used to price step options and the particular case of an exponential spectrally negative Levy jump-diffusion model is discussed.

引用

页码：274 / 297

页数：24

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