The Valuation of Convertible Bonds with Numeraire Changes  

作　　者：Hai-lin Zhou Shou-yang Wang 

机构地区：[1]School of Economics and Management, Beihang University, Beijing 100191, China [2]School of Finance, Anhui University of Finance and Economics, Bengbu 233041, China

出　　处：《Acta Mathematicae Applicatae Sinica》2010年第2期321-332,共12页应用数学学报（英文版）

基　　金：Partially supported by the National Nature Science Foundation of China;The Research Grants Council of HongKong Grant (No. 70731160635)

摘　　要：The changes of numeraire can be used as a very powerful mean in pricing contingent claims in the context of a complete market. We apply the method of nurmeraire changes to evaluate convertible bonds when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds follow a general adapted stochastic process in this paper. A closed-form solution is derived when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds are deterministic function of time. We also consider a special case when the asset price follows GBM （Geometric Brownian Motion） and interest rate follows Vasicek＇s model.The changes of numeraire can be used as a very powerful mean in pricing contingent claims in the context of a complete market. We apply the method of nurmeraire changes to evaluate convertible bonds when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds follow a general adapted stochastic process in this paper. A closed-form solution is derived when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds are deterministic function of time. We also consider a special case when the asset price follows GBM （Geometric Brownian Motion） and interest rate follows Vasicek＇s model.

关 键 词：Convertible bonds complete market numeraire changes closed-form solution 

分 类 号：O211.3[理学—概率论与数理统计] F832.5[理学—数学]