A Green’s Function for a Convertible Bond Using the Vasicek Model
نویسندگان
چکیده
A convertible bond is defined to be (e.g., Jorion [10]) a bond issued by a corporation that can be converted into the equity of that corporation at certain times using a predetermined exchange ratio. This entails the creation of new shares issued by the corporation if and when conversion occurs, and the existing shares are diluted by the creation of the new shares. The option to convert is solely at the discretion of the bond holder who will do so only if it is beneficial. Typically, firms issue convertible bonds because they offer a lower interest cost and less restrictive covenants than a nonconvertible bond, but the drawback is that the issuer will be confronted with capital structure uncertainty. Convertible bonds are often subordinated debentures, and because of this, the bond rating agencies have usually rated convertibles one class below that of a straight debenture (Dialynas et al. [7]), and typically issuing convertibles will not affect a company’s rating. In return for a reduced yield, an investor will receive a security with considerable upside potential along with downside protection. Conceptually, the behavior of a convertible bond can be segmented into four regions (e.g., Dialynas et al. [7]). In the late 1990s, most new
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