基于倒向随机微分方程理论的可分离债券定价  

Pricing of Equity Warrant Bond Based on the Theory of Backward Stochastic Differential Equations

作　　者：苗杰 MIAO Jie(School of Mathematics,Guangdong University of Education,Guangzhou 510303)

机构地区：[1]广东第二师范学院数学学院,广州510303

出　　处：《工程数学学报》2022年第3期487-494,共8页Chinese Journal of Engineering Mathematics

基　　金：2021年教育部产学合作协同育人项目(202102496004);广东省自然科学基金(2017A030310609);2019年度校级教学质量与教学改革工程项目(2019jxgg10)。

摘　　要：倒向随机微分方程理论搭起了随机与确定之间的桥梁,使人们可以用确定的策略方法去解决随机的不确定性问题,为金融产品的定价开辟了一条新的路径。因此,利用倒向随机微分方程理论研究了可分离债券的定价问题。首先,假设市场是无套利的,合理地建立了投资组合,通过自融资策略,用倒向随机微分方程理论得到了可分离债券价格所满足的倒向随机微分方程。接着,用非线性Feynman-Kac公式,得到了可分离债券价格所满足的偏微分方程,并证明了可分离债券在0时刻的价格等于到期现金流的条件期望,用鞅的方法得到了可分离债券价格的显示公式。最后,以马钢可分离债券为例进行实证分析,验证了本文得到的定价模型更合理。The backward stochastic differential equation theory builds a bridge between randomness and certainty, which makes it possible for using deterministic strategies to solve random and uncertain problems, and opens up a new way for the pricing of financial products.Thus, the pricing problem of equity warrant bond is studied by using the theory of backward stochastic differential equations. Firstly, under the no arbitrage assumption, the portfolio is reasonably established. Through the self-financing strategy, we derive a backward stochastic differential equation that the price of equity warrant bond satisfies by using the backward stochastic differential equation theory. Then, using the nonlinear Feynman-Kac formula, we get a partial differential equation that the price of equity warrant bond follows, and it is proved that the price of equity warrant bond at time 0 is equal to the conditional expectation of the maturity cash flow. The explicit formula for the price of an equity warrant bond is obtained by the martingale method. Finally, taking the equity warrant bond of Masteel as an example, the empirical analysis verifies that the pricing model obtained in this paper is reasonable.

关 键 词：可分离债券 倒向随机微分方程 Feynman-Kac公式 自融资策略 

分 类 号：O211.63[理学—概率论与数理统计]