基于单因子混合分布的BDS定价模型  

The model for BDS pricing based on single factor mixture distribution

作　　者：赵雪妮[1] 张茂军[1] 王文华[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2013年第6期508-513,共6页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(71001015;71101033);广西自然科学基金(2012GXNSFAA053013);广西教育厅科研项目(201106LX162)

摘　　要：针对一篮子信用违约互换(BDS)定价问题,建立了单因子正态逆高斯混合分布模型,并给出违约时间的分布函数和密度函数,利用计算顺序统计量方法得到第k次违约时间的分布函数。根据风险中性定价原理,给出第k个参照实体违约时的BDS价格解析式。提出的模型刻画了BDS参照实体违约时间分布的尖峰厚尾特征,使其更加符合违约时间数据的真实特性。研究表明,用顺序统计量方法计算BDS的理论价格,能简化其定价过程,为投资者提供了一种新的定价方法。Aiming at a basket default swap（BDS）pricing,a single factor model with the mix-distribution of standard Gaussian and inverse Gaussian is made in the paper.The density function and distribution function of the default time are given and the explicit formula for the distribution of the k-th default time is obtained by the method for calculating of order statistics.The closed form of the price of BDS at the k-th is calculated by using the risk-neutral pricing principle.The proposed model describes distribution＇s fat-tail character of the reference entities＇ default time,which makes it be more in line with the real property of default time data.Using the proposed order statistic method to calculate the theoretical BDS pricing,the process of pricing is simplified,and a new pricing method is provided for traders.

关 键 词：信用违约互换 顺序统计 单因子模型 正态-NIG混合分布 资产定价 

分 类 号：O235[理学—运筹学与控制论] F380[理学—数学]