Copyright © 2011 Huiwen Yan and Fahuai Yi. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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