中文摘要：

可转换债券（以下简称可转债）是一种兼具权益性和债务性的复杂的混合金融工具，近些年发行的可转债条款日益复杂，里面嵌入了多种期权，如赋予发行者的赎回权、转股价格向下修正权，赋予投资者的转股权、回售权，以及转股封闭期和赎回通知期等。这些权利之间的相互作用，造成了可转债定价的高度复杂性和挑战性。这之前的可转债定价模型多将嵌入的各种期权进行简单的静态加总，忽略了期权之间的相互影响的效应，而且很多研究为了降低模型难度，多将嵌入的各种期权处理为欧式期权或美式期权，这些做法都与市场中真实的可转债条款存在较大差异，从而造成了较大的定价偏差，应用价值较低。本文的研究也无法涵盖可转债条款中所有嵌入期权的情况，而是主要研究可转债的赎回、转股和回售条款之间的博弈，引入美式博弈期权概念，在数学建模方面选择了双反射壁倒向随机微分方程，并在一定假设条件下将双反射壁倒向随机微分方程转换成相应的变分不等式进行求解。最后，选择我国内地可转债市场上的9支可转债进行实证分析，具体选择了时间序列数据和横截面数据两种类型的样本。实证结果与实际值相比，误差较小，充分表明该定价模型良好的适用性，提升了可转债定价模型研究的理论深度，也为发行者和投资者的融资和投资行为提供了较好的决策依据。

英文摘要：

Convertible bond is a hybrid financial instrument with equity and liability property. It is also a complicated embedded option security. Convertible bond has many provisions, which include call right, put right and conversion right. The complication of convertible bond induces the complexity of its pricing. In this paper, when we deal with the game between the call clause and the put clauses, we consider it as American option game. We use the Reflected Backward Stochastic Differential Equation with two barriers （R2BSDE） to model the convertible bond pricing. Under some assumptions, we transform the R2BSDE to a related variational inequality for numerical analysis. We choose several real convertible bonds data from China Mainland capital market for empirical analysis. Including time series data and cross-section data. Both empirical results show that the pricing model fit the market price pretty well. The proposed pricing model could be a good guide for convertible bond issuers and investors.