杨瑞成,秦学志,陈田.随机相关结构下单因子混合高斯模型的CDO定价问题[J].,2009,(4):587-593 |
随机相关结构下单因子混合高斯模型的CDO定价问题 |
Valuation of CDO based on single factor Gaussian mixture model with stochastic correlation structure |
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DOI:10.7511/dllgxb200904021 |
中文关键词: 债务抵押证券 混合高斯分布 随机相关结构 分券层 信用价差 |
英文关键词: collateralized debt obligation (CDO) Gaussian mixture distribution stochastic correlation structure tranche credit spread |
基金项目:国家自然科学基金资助项目(70771018);中国博士后科学基金资助项目(20070410350);教育部人文社会科学基金资助项目(05JA62905);教育部新世纪优秀人才计划联合资助项目(2005). |
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中文摘要: |
CDO是近十年来发展最为迅速的信用衍生产品之一,其核心问题为如何对CDO分券层进行定价.基于此,通过引进混合高斯分布建立了随机相关结构条件下的单因子混合高斯定价模型,进一步给出了单个资产违约的概率分布,据此得出了整个资产池累积违约损失的概率分布,并分别得出了基于伯努利随机相关结构和对称随机相关结构条件下的具体表达形式.在分析CDO分券层损失面的预期损失和收益面的预期收入的基础上,利用无套利定价原理得出了CDO分券层的合理信用价差. |
英文摘要: |
CDO is one of the most popular credit derivative products during the latest ten years, and the key issue is how to price the tranche. For solving this problem, by introducing the mixed Gaussian distribution, the single factor Gaussian mixture model with the stochastic correlation structure is established. Furthermore, the probability distribution of single asset is given, and the probability distribution of cumulative default loss of the whole portfolio pool is derived. At the same time, the explicit forms on Bernoulli stochastic correlation structure and symmetric stochastic correlation structure are obtained. Besides, based on analyzing the expected default leg and premium leg, according to the arbitrage-free principle, the fair credit spread of CDO tranche is derived. |
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