Application Of Finite Element Method On Convertible Bonds Valuation

Convertible bonds appear in China security market for few years, and which have become an important type of financing instrument. It is of great significance to evaluate convertible bonds for issuing company designing issuance provisions, investors making decision reasoningly, and convertible bonds market developing healthily. As a derivative security, convertible bond has the characters of bond and stock. So the pricing of convertible bonds is very complex. There are many factors that should be considered, such as stock price, interest rate, credit risk, maturity date, etc. In addition, the attached provisions are important, such as callability provision and putability provision, and which make the pricing of convertible bonds more difficult. The early conversion provision, callability provision and putability provision are treated in the boundary conditions of valuation problem. Those provisions all have American feature, so the valuation of convertible bonds is corresponding to a free boundary problem, which must be solved by numerical methods. In the pricing of convertible bonds, finite difference method is often used. To provide a new way, finite element (FE) method is applied to solved those valuation models, which has some clear advantages over finite difference method: FE can deal with any solution domain, FE provide accurate Greeks (risk management parameters) as a by-product, and FE provide more flexibility in terms of incorporating final conditions and handling boundary conditions. Further more, a valuation model for convertible bonds with credit risk, which was first presented by Tsiveriotis and Fernandes (1998), is introduced in this paper. This model divides convertible bond into two parts: one is the bond part that suffers from credit risk; the other is the stock part that doesn't suffer from credit risk. In this model, credit risk is described by a constant credit spread, but the constant credit spread can't reflect the influence of underlying stock price and its determination is difficult. To overcome these drawbacks, a function of credit spread is presented, which is based upon the structural model of credit risk. This function that can reflect the influence of underlying stock price is used to replace the constant credit spread. As a result, a more elaborate convertible bond valuation model is obtained. At last, an investigation of the pricing of Min Sheng convertible bond, using daily market prices for a period from 14 Mar. 2003 to 19 Dec. 2003, is implemented.