14:15
A firm issues a convertible bond. At each subsequent time, the bondholder
must decide whether to continue to hold the bond, thereby collecting coupons, or
to convert it to stock. The bondholder wishes to choose a conversion strategy to
maximize the bond value. Subject to some restrictions, the bond can be called by
the issuing firm, which presumably acts to maximize the equity value of the firm
by minimizing the bond value. This creates a two-person game. We show that if
the coupon rate is below the interest rate times the call price, then conversion
should precede call. On the other hand, if the dividend rate times the call
price is below the coupon rate, call should precede conversion. In either case,
the game reduces to a problem of optimal stopping. This is joint work with Mihai
Sirbu.