Quantitative Models to Value Convertible Bonds
Abstract: Convertible bonds are bonds that give their holders the right to periodic coupon payments and, as of a fixed date, the right to convert the bonds into a fixed number of shares. If the bondholder decides to exercise his conversion right, instead of being paid back the par value of the bonds, he will receive a fixed number of shares in exchange. There are several options embedded in a convertible bond. There is obviously a call option on the underlying stock. All convertible bonds are callable. A convertible bond may be putable. The presence of all of these options complicates the valuation of convertible bonds. There are models that practitioners use for valuation purposes. These models are classified as analytical models and numerical models.
Convertibles are ideal securities for arbitrage, because the convertible itself, namely the underlying stock and the associated derivatives, are traded along predictable ratios, and any discrepancy or misprice would give rise to arbitrage opportunities for fund managers. Traders use quantitative models to identify convertible bonds whose market value differs from their theoretical price. However, unlike callable bonds or putable bonds that have interest rate–embedded options, a convertible bond also has an embedded equity option. This complicates the quantitative modeling of these securities.