| With the increasing integration of global finance and the fast development of Chinese economic, it is very necessary for China to develop derivatives markets. Given the hybrid feature of containing elements of both debt and equity, convertible bonds are sophisticated derivatives that provide investors with both the downside protection of ordinary bonds and the upside return of equities. After Management Regulation of Convertible bonds is issued, Chinese market of convertible bonds has been developing quickly. Based on the data from stock exchanges, in Chinese capital market, the total sum of convertible bonds issued in 2003 is not only greater than the total sum of placement of A shares in the same year, but also the total sum of seasonal equity offering of A shares. Without doubt, it has already become one of main financing channels for the listed companies to issue convertible bonds.However, convertible bonds are sophisticated financial instruments involving simultaneously bonds, equities and options such as convertible options and callable options. It is very difficult to value them. In the developed capital market, they are generally valued with numerical methods, including binomial tree, finite difference methods, finite element methods, Monte Carlo simulation and so on. However, their valuation efficiency is not high enough, especially in current information age. As we know, the analytic solution is the highest efficient method. Until now, some analytic solutions for relatively simple convertible bonds have already been worked out. However, they are impractical because they are based on the assumption that the underlying asset is firm value.In this dissertation, after having summed up the literatures of valuing convertible bonds in the past more than 40 years, according to the features of relative regular clauses of convertible bonds, based on the risk-neutral pricing principle, a series of analytic formulae have been worked out for the different complex convertible bonds from simple to complex by regarding stock price as the underlying asset and employing the complete decomposition pricing method and martingale pricing method. Without doubt, as convertible bonds become complex, the analytic formulae would seem more and more complicated, but in fact the parameter estimations and preconditions about capital markets that they require are the same as Black-Scholes option pricing formulae. Therefore, widespread use of these formulae in practice could be expected. Compared with previous analytic formulae, they are more practical because stock price instead of firm value is regarded as the underlying asset. Compared with the existing numerical pricing methods, they can greatly speed up the valuation of convertible bonds and the calculation of their important Greeks for risk management. Therefore, these formulae must be very helpful for Chinese investors to reasonably and conveniently price convertible bonds. At the same time, by employing the complete decomposition method proposed in this dissertation, value components of basic convertible bonds (no other embedded option except the convertible option) and callable convertible bonds can be analyzed reasonably and easily, and their risk can be better hedged. Besides, this dissertation analyzes in detail the effect of coupon clauses, screw clauses, call clauses, soft call condition clauses, hard call clauses, put clauses and credit risk. Obviously, these can give Chinese investors a lot new insights into the analysis of the convertible bonds.The main work and conclusions are as follows:1. We sum up the literatures in the past more than 40 years, and classify main existing valuation models into five types: one-factor (firm value) arbitrage-free model, two-factor (firm value and interest rate) arbitrage-free model, one-factor (stock price) arbitrage-free model, two-factor (stock price and interest rate) arbitrage-free model, credit-risk arbitrage-free models.2. By employing the complete decomposition pricing method, we valuate and analyze the basic convertible bonds. First, based on the risk-neutral pricing principle, we completely decompose them into two kinds of simpler securities: corresponding ordinary bonds and European warrants. Second, we work out the analytic formulae for them. Third, we validate these formulae with Monte Carlo simulation. Furthermore, we display the three-dimensional relationships between their value and two state variables, and between the value of their embedded option and two state variables. Besides, we analyze in detail the effect of coupon clauses and screw clauses.3. By employing the complete decomposition pricing method, we valuate and analyze the zero-coupon callable convertible bonds without soft call condition clauses. First, based on the risk-neutral pricing principle, we completely decompose them into five kinds of simpler securities: corresponding ordinary discount bonds, two kinds of regular American binary calls with different immediately-made fixed payments, regular up-and-out calls and regular American binary calls with a fixed payment deferred until maturity. Second, we work out the analytic formulae for them. Third, we validate these formulae with Monte Carlo simulation. Furthermore, we display the three-dimensional relationships between their value and two state variables, between the value of their embedded option and two state variables, and between the value of every one of these five kinds of simpler securities and two state variables. Besides, we analyze in detail the effect of call clauses without soft call condition clauses and the valuation errors of two previous decomposition pricing methods.4. By employing the complete decomposition pricing method, we valuate and analyze the coupon-bearing callable convertible bonds without soft call condition clauses. First, based on the risk-neutral pricing principle, we completely decompose them into seven kinds of simpler securities: corresponding ordinary coupon-bearing bonds, two kinds of regular American binary calls with different immediately-made fixed payments, regular up-and-out calls, two kinds of regular American binary calls with different fixed payment deferred until maturity and non-regular American binary calls with an immediately-made fixed payment. Second, we work out the analytic formulae for them. Third, we validate these formulae with Monte Carlo simulation. Furthermore, we display the three-dimensional relationships between their value and two state variables, between the value of their embedded options and two state variables, and between the value of every one of these seven kinds of simper securities and two state variables. Besides, we analyze in detail the effect of call clauses without soft call condition clauses and the total effect of both coupon clauses and screw clauses.5. By employing the complete decomposition pricing method, we valuate and analyze the complex default coupon-bearing callable convertible bonds without soft call condition clauses. First, similar to the case above of no credit risk, we completely decompose them into seven kinds of simpler securities, but their parameters are different from those in the case of no credit risk. Second, we work out the analytic formulae for them. Third, we validate these formulae with Monte Carlo simulation. Furthermore, we display the three-dimensional relationships between their value and two state variables, between the value of their embedded options and two state variables. Besides, we analyze in detail the effect of credit risk.6. By employing the complete decomposition pricing method, we valuate and analyze the fairly complex default coupon-bearing callable convertible bonds with soft call condition clauses. First, similar to the case above of no soft call condition clauses, we completely decompose them into seven kinds of simpler securities, but their parameters are different from those in the case of no soft call condition clauses. Second, we work out the analytic formulae for them. Third, we validate these formulae with Monte Carlo simulation. Furthermore, we display the three-dimensional relationships between their value and two state variables, between the value of their embedded options and two state variables. Besides, we analyze in detail the effect of the soft call condition clauses.7. By employing the martingale pricing method, we valuate and analyze the more complex default coupon-bearing callable convertible bonds with both soft call condition clauses and hard call condition clauses. First, according to the possible four cases of their ending, we completely decompose them into four relative simple parts. Second, we work out the analytic formulae for them. Third, we validate these formulae with Monte Carlo simulation. Furthermore, we display the three-dimensional relationships between their value and two state variables, between the value of their embedded options and two state variables. Besides, we analyze in detail the effect of the hard call condition clauses.8. By employing the martingale pricing method, we valuate and analyze the further more complex puttable callable convertible bonds with soft call condition clauses and soft put condition clauses. First, according to the possible four cases of their ending, we completely decompose them into four relative simple parts. Second, we work out the analytic formulae for them. Third, we validate these formulae with Monte Carlo simulation. Furthermore, we display the three-dimensional relationships between their value and two state variables, between the value of their embedded options and two state variables. Besides, we analyze in detail the effect of the soft put condition clauses.9. With the sample of YAGE convertible bond between February 16, 2004 and February 16, 2006, we give the empirical research with Monte Carlo simulation and the analytic formulae obtained in the chapter 8 for the complex puttable callable convertible bonds with soft call condition clauses and soft put condition clauses. Furthermore, we adopt GARCH(1,1) model and weekly data instead of daily data to estimate the volatility of the underlying stock price. From the empirical research, we find that the mean of percentage errors of theory prices from the analytic formulae relative to market prices is only 2.45%, and the former traces the latter very well for their correlation coefficient reaches 0.9512。Besides, we also demonstrate the sensitivities of the value of YAGE convertible bond to estimated parameters and the effects of various clauses and credit risk respectively.The primary innovations in this dissertation are summarized in the following.1. By using the complete decomposition pricing method, decompose the basic convertible bonds into two kinds of simple tradable securities, obtain their analytic formulae. Besides, analyze the effect of coupon clauses and screw clauses.2. By using the complete decomposition pricing method, decompose the zero-coupon callable convertible bonds into five kinds of simpler tradable securities, the coupon-bearing callable convertible bonds into seven kinds of simpler securities, and the default coupon-bearing callable convertible bonds into seven kinds of simpler securities too. Furthermore, obtain their analytic formulae respectively. Besides, analyze their value components and the effect of call clauses without soft call condition clauses, the effect of both coupon clauses and screws clauses, and the effect of credit risk respectively.3. By using the modified credit spread approach and the complete decomposition pricing method, decompose the default coupon-bearing callable convertible bonds with soft call condition clauses into seven kinds of simpler securities, and obtain their analytic formulae. By employing martingale pricing method, obtain analytic formulae for the default coupon-bearing callable convertible bonds with both soft call condition clauses and hard call condition clauses. Besides, analyze the effect of the soft call condition clauses and the effect of the hard call condition clauses respectively.4. By employing martingale pricing method, obtain analytic formulae for the puttable callable convertible bonds with both soft call condition clauses and soft put condition clauses. Besides, analyze the effect of the put clauses with the soft put condition clauses.5. With the sample of YAGE convertible bond, demonstrate the empirical research by using the analytic formulae worked out in this dissertation for the puttable callable convertible bonds with both soft call condition clauses and soft put condition clauses. |
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