The Study On The Pricing Of Several Special Types Of Convertible Bond

The Convertible Bond is a kind of rather complicated financial derivatives.Besides the common debt,it includes many options,such as conversion option ,call option ,put option and the lower conversion price option.The complexity of clauses in Convertible Bond results in the difficulties of Convertible Bond pricing. Black-Scholes option pricing model is one of the most important theory in modernnancial realm, which succeeds in pricing Convertible Bond.The most popular pricing model of Convertible Bond is the one factor pricing model with the price of the stock as the basic variable,in which the valuation of theConvertible Bond is denoted as the sum of the valuation of a common bond and a call option. Because of the complexity, the results of the two factor pricing model with the price of the stock as the basic variable which considered both the change of the price of the stock and the interest rate, is not ideal.First ,the structure clauses and the factors which affect the valuation of theConvertible Bond are simply introduced: Second ,the classical pricing methods of the Convertible Bond: Ingersoll's one factor model and Brennan & Schwartz's two factor model, the widely used model:simplified one factor model and simplified two factor model, and the pricing model of numerical method: two binomial tree model and Monte Carlo simulation, are introduced in detail.In the end ,this paper trys to price the Convertible Bond based on the other people' results.In so many kinds of convertible pricing models,the using of martingale method can never be seen frequently. Based on the characters of the Convertible Bond under Chinese markets and the results of other people, with martingale methods ,this paper trys to pricing Convertible Bond under three conditions :Convertible Bond with no back buy treaty and no back sell treaty,with back buy treaty,with back sell treaty under the assumption that: the market is completed and continuous ,the price of the Convertible Bond is a function of the price of the stock ,the stock has dividend-paying and has the expected yieldμ(t) ,fluctuationσ(t) ,dividendρ(t) ,which all depend on t .Compared with other models ,the characters of Chinese markets and the credit risk are considered in the model of this paper.The main results and innovation is as follows:1.Under the assumption that the Convertible Bond can not be bought back,the pricing formula(4-3) of the Convertible Bond is deduced based on the martingale method,the conclusion of the article [23] is extended.By using (credit spread +risk-free rate ) as the discount factor of the part of the future cash payment ,the credit risk is introduced in the model of this paper,then the pricing formula (4-4) with credit risk is derived.2.As the back buy treaty is that : In the bond-hold period [0, T,]f the highest price of the stock broke through the barrier price L ,the company that issued the ConvertibleBond can enforce the convertible bond holder to immediately carry out their conversion option, the pricing formula(5-4) of Convertible Bond with back buy treaty is evolved, the conclusion of the article [39] is extended and then the pricing formula(5-5) with credit risk is evolved.3. As the back sell treaty is that : In the bond-hold period [0, T,]f the lowest price of the stock broke through the barrier price B ,the convertible holder may have three choices ,that is :they can immediately sell the Convertible Bond to the company that issued the Convertible Bond ,they can remain hold bonds to maturity then sell(but the interest rate is market rate),or they can convert it into stocks at the lowed convertible price. The pricing formula[6-4] of Convertible Bond with back sell treaty is evolved,and then considering the credit risk, the pricing formula(6-5) with credit risk is evolved.