The Pricing Of Convertible Bonds In Chinese Market

Convertible bonds are specific derivatives which possess the mixing feature of equity and bond. The issuer can meet his own financing standard by combining different clauses, and also provide investors with a special product. The high flexibility presents a great challenge for rational pricing.There doesn’t exist a single model which could reflect all possible clauses. When trying to price a pecific convertible bond, we should check the clauses according to the features of different markets, and base our model on a sound assumption.We think the most important feature of the convertible bonds in Chinese market is that there exist mandatory requirements concerning call/put option, and the trigger condition of call/put option is path-dependent. Then we conclude that, the pricing of convertible bonds in Chinese market can be transformed from a two-person game option to a optimal decision problem. The path-dependency assumption is the main difference with other thesis on pricing convertible bonds in Chinese market. We will show that the omission of this assumption could present significant bias which makes the theoretical value lower.We adopt methods fitting the reality of Chinese financial market in the implementation of our model.As there is no referable implied volatility in China, we construct a stochastic model of volatility with GARCH model. We could relate the dynamic progress of stock price in risk-neutral measure with the volatility model in real-world measure by a parametric which is named as the market price of risk. In such setting, the conditional volatility progress will be drived by the same Brownian motion of stock price. With this method, the model could better reflect the feature of volatility-clustering, and be more close to reality.We use reduced-form method to price the default risk of convertible bonds. Because of the lack of a credit derivative market, we use the yield curve of the bonds with same rating as convertible bonds, and the yield curve of sovereign debt to construct the defaultable zero-coupon bond, which could be used for estimating the intensity. The model of default risk could integrate well with the initial default-free model.We also consider the impact of stochastic risk-free rates on the valuation result. To estimate the parameters of the CIR short rate model, we adopt the non-parametric methods proposed by Ait-Sahalia in1996. We also check the difference of theoretical values be-tween a stochastic rate model and a fixed rate model. The result shows that we could omit the impaction of the stochastic rate, when pricing convertible bonds in Chinese market.At last, we price some actively-traded convertible bonds with the model proposed.The result shows that the theoretical value fits the market value very well when the stock price at the money.