A Variational Inequality from Pricing Convertible Bond

Advances in Difference Equations

Huiwen Yan¹  Fahuai Yi¹ 

[1] School of Mathematics, South China Normal University, Guangzhou, China

关键词: Variational Inequality;    Free Boundary;    Stock Price;    Comparison Principle;    Bond Price;   

DOI  :  10.1155/2011/309678

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY