previous up next SYLLABUS  Previous: 2.2.4 Bond options: caps,  Up: 2 A VARIETY OF  Next: 2.4 Hedging parameters, portfolio


2.3 Convertible bonds

[ SLIDE convertible || same VIDEO as previous section modem - LAN - DSL ]

A convertible bond has many features of a regular bond with payment of coupons at regular intervals, except that the holder has the right anytime to exchange the principal for a given asset. When it reaches maturity at time $ T$ , the convertible bond returns an amount $ A$ unless the owner has converted the bond into $ n$ shares of the underlying with a total value $ nS$ . Immediately before maturity, the payoff is described by

$\displaystyle \Lambda_\mathrm{convertible}=\mathrm{max}(A,nS).$ (2.3#eq.1)

Although the terminal payoff in (2.3#fig.1) does not present much difficulty, the valuation of a convertible bond before the expiry is substantially complicated by the long time spans under consideration: a proper model involves two imperfectly correlated random variables describing fluctuations in the stock $ S(t)$ and bond prices $ r(t)$ .
Figure 2.3#fig.1: Terminal payoff diagram for a convertible bond with a principal $ A$ as a function of possible realizations of the underlying share price $ S$ .
\includegraphics[height=3.8cm]{figs/payConvertible.eps}

SYLLABUS  Previous: 2.2.4 Bond options: caps,  Up: 2 A VARIETY OF  Next: 2.4 Hedging parameters, portfolio