可转换公司债是一个兼具股票性和债券性的金融产品，其定价则是一个受到广泛研究的课题。一方面可转债的推出丰富了市场的金融产品种类，投资者可以有更多的选择来进行资产配置，实现风险分散；另一方面发行人在条款的设计上也愈加多样和巧妙，良好的定价可以更加合理的调整公司的融资结构，推动公司股价上涨。

在学界，由于可转债所蕴含的衍生品的属性，其定价方法的逐步演化也一定程度上依赖期权定价手段的发展。从最早将可转债看成投资价值和转换价值的简单组合，到20世纪70年代中期Black-Scholes的问世，再发展到后来基于股价变动和利率变动的双因素模型，可转债的数值求解变得越来越准确。

本文基于二叉树模型对可转债定价问题进行研究，主要是考虑到其相比于传统的定价方法有较强的实用性。在理论模型构建部分，我先单独介绍了基于股票和债券的二叉树模型，然后再考虑将二者融合，结合可转债的基本条款，给出了在二叉树具体节点上的价值选取公式以及条款实现背后的经济学意义。在实证分析部分，我选取了最近发行的白云转债作为案例进行分析，并在理论模型的基础上进行了一定程度的简化。在具体的估计了参数后，得出了其上市交易日的理论价格。比对发现，我计算得到的理论价格高于实际价格，分析其可能是由于债券市场流动性较差、模型基于的利率期限结构平坦假设和股票波动率估计不够准确导致的。

关键词：可转换债券；定价模型；二叉树

Convertible Bonds is a kind of rather complicated derivatives, which has the characteristics of both common bonds and stocks. Extensive Research has been made in the field of Convertible Bond pricing. It is one of the creative financial tools in the capital market. On one hand, the investors can have more choices in asset allocation and risk dispersion. On the other hand, benefited from ingenious and diversified product design, the issuers can make more reasonable judgments in the field of financial structure, promoting the company shares rising.

In the academic circles, because of the derivative property, the gradual evolution in of the pricing method in convertible bond pricing depends largely on development of the option pricing model. The earliest model can be as simple as seeing convertible as a combination of the investment value and convertible value. Afterwards, the advent of Black-Scholes in the middle of 1970s becomes a significance milestone of the derivative pricing. Later on, the two-factor model based on stock price and interest rate has been introduced, and the numerical solution has made the pricing model more empirically accurate.

In this paper, the study of convertible bond is based on the binary tree pricing model, which, compared with the traditional pricing model, is more practical to some extent. In the part of theoretical model construction, I introduce derivatives pricing based on stocks and bonds using the binominal tree method. Then I illustrate the approach of how to select the value on each node of the binominal tree. Finally I explain its economic meaning behind each special provision. In the third part of empirical analysis, I simplify the theoretical model appropriately, and enact it into a specific case. Then I compare my theoretical price with the current market price, and some possible reasons of the phenomenon are given.

Key Words: Convertible Bonds；Pricing Model；Binominal Tree

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