Credit Spread Implied by Convertible Bonds Prices

Although many credit risk models exist in the academic literature, little attention has been paid to the measurement of credit spread, which is an important input in most of those models. When a reference entity has not issued any straight bond it becomes impossible to calculate credit spread and consequently to exploit credit risk models. This article derives a method for measuring the credit spread implied by convertible prices using Tsiveriotis and Fernandes (1998) model, which account for the influence of credit spread on the convertible value. This approach allows measuring the credit spread in cases where a reference entity has issued convertible bonds and not straight bonds. The spread between a corporate bond and a default free bond is driven to a considerable extent by credit risk, but also the liquidity premium has a great impact on that spread. Using the suggested method in cases where company's convertible bonds are significantly more liquid than its straight bonds may lead to a more accurate measurement of the credit spread. In this paper we also elaborate and present more abstract way Hull (2000) numerical scheme for pricing convertible bonds according to Tsiveriotis and Fernandes (1998) model. Numerical example is provided to show how to calibrate the pricing model and to illustrate the calculation of the implied credit spread.