bankruptcy valuation
A convertible bond is a hybrid derivative with complex embedded features. It allows a holder to convert a bond to certain shares (conversion ratio) of stock issued by the same company at a prescribed stock price (conversion price). Besides, it normally has an embedded call (put) option which allows a bond issuer (holder) to call (sell) back it from the holder (to the issuer) at a pre-decided call (put) price once the underlying stock price is above (below) the strike price for a certain prescribed, consecutive time, hereafter called a Parisian option. In Asian markets, it also has a refix clause which allows the bond issuer to reset the conversion price, under several stock price scenarios. As a hybrid product with equity and fixed income characteristics, convertible bond is under a default risk, and both stochastic interest rates and stochastic volatility play roles in its valuation.
These factors make convertible bond pricing complicated: one popular method is to choose two or three important modelling factors, and often numerical calculation is applied to solve this problem, for instance,by Monte Carlo simulation and binomial tree. However, both methods are either too time consuming or too inaccurate to satisfy the needs of financial industry.
Tsiveriotis and Fernandes (1998) at their paper “Valuing Convertible bonds with credit risk” published in the Journal of Fixed Income value the convertible bond price with credit risk via a finite difference method, by dividing it into cash-only and equity parts, where different discount rates are used. This method gradually becomes the standard of convertible bond valuation and widely accepted by both industry and academia.
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