可转换债券中一类两期双边障碍巴黎期权的定价  

Pricing Two-period Double Barrier Parisian Options of Convertible Bonds

作　　者：李静[1] 程希骏[1] 张青[1] 

机构地区：[1]中国科学技术大学统计与金融系,合肥230026

出　　处：《工程数学学报》2013年第3期361-369,共9页Chinese Journal of Engineering Mathematics

基　　金：中国科学院知识创新工程重要方向资助项目(KJCX3-SYW-S02)~~

摘　　要：本文研究可转换债券中嵌入的一类路径相关期权定价问题.尽管偏微分方程数值解方法可以获得这类期权的价格,然而数值算法的收敛速度很慢.为了获得快速而有效的定价方法,本文将可转换债券中的期权简化为两期双边障碍巴黎期权,并给出了这类两期双边障碍巴黎期权的风险中性价格关于到期时刻的Laplace变换.基于Euler数值逆算法求解了数值例子,数值结果表明该数值算法快速、稳定和有效.This paper considers the pricing problem of a kind of path dependent options em- bedded in convertible bonds. Although the option prices can be obtained by solving associated partial differential equations numerically, the convergence rate is very slow. To obtain a fast and efficient pricing method, we first simplify these options into a class of two-period double barrier Parisian options, and then provide the Laplace transform formulas of neutral-risk prices of these two-period double-barrier Parisian options with respect to the maturity time. Also nu- merical results of an example are provided by using the Euler algorithm of numerical inversion of the Laplace transform. The numerical results show that the Euler algorithm is fast, stable and efficient.

关 键 词：可转换债券 巴黎期权 BROWNIAN MEANDER LAPLACE变换 Euler算法 

分 类 号：O211.9[理学—概率论与数理统计]