文章基本信息

标题：A Variational Inequality from Pricing Convertible Bond
本地全文：下载
作者：Huiwen Yan ; Fahuai Yi
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2011
卷号：2011
期号：1
页码：309678
DOI：10.1155/2011/309678
语种：English
出版社：Hindawi Publishing Corporation
摘要：The model of pricing American-style convertible bond is formulated as a zero-sum Dynkin game, which can be transformed into a parabolic variational inequality (PVI). The fundamental variable in this model is the stock price of the firm which issued the bond, and the differential operator in PVI is linear. The optimal call and conversion strategies correspond to the free boundaries of PVI. Some properties of the free boundaries are studied in this paper. We show that the bondholder should convert the bond if and only if the price of the stock is equal to a fixed value, and the firm should call the bond back if and only if the price is equal to a strictly decreasing function of time. Moreover, we prove that the free boundaries are smooth and bounded. Eventually we give some numerical results.
关键词：Variational Inequality ; Free Boundary ; Stock Price ; Comparison Principle ; Bond Price