Convertible Bonds with Call Notice Periods
Andreas J. Grau
Peter A. Forsyth
Kenneth R. Vetzal
School of Computer Science
University of Waterloo, Canada
In practice, convertible bonds can often be called only if notice is given to the holders.
Most methods for valuing convertible bonds assume that the bond is continuously callable.
In this paper, we develop an accurate PDE method for valuing convertible bonds with a finite
notice period. Example computations are presented which illustrate the effect of varying notice
periods. The results are compared with a recently published approximation method.
Convertible bonds (or convertibles) have become an important instrument in the financial markets.
Having properties of both stocks and bonds, convertible bonds can be an attractive alternative for
investors. Studies suggest that the average return of convertible bonds in the last few years were as
high as the returns of the stock market, although they incorporate a lower risk [vdHKL02, LR93].
There are different reasons for a company to issue convertible bonds. Tax considerations in some
countries lead to an advantage in issuing convertibles instead of bonds. Another possibility is that
a small, fast growing company needs a debt but has poor credit rating.
The convertible bond market is not as standardized as the exchange traded stock market. Con-
vertibles can incorporate a variety of features. The instrument might be convertible into shares of
the issuing company or in some cases into shares of a different company. Usually convertibles may
be converted by the holder at any time. Often, these bonds can be put to the issuer at specific dates
for a guaranteed price. In addition, the issuer may have the right to redeem the convertible at a call
price or force a conversion into stocks. To keep the convertibles attractive in this case, so called
soft and hard call constraints are devised. The hard call constraint prohibits a forced conversion in
the initial life of the contract. The soft c