基于因子Copula的CDO定价模型及数值分析

发布时间：2018-04-25 01:12

本文选题：单因子Copula模型 + 大样本同质投资组合(LHP)　；参考：《浙江工业大学》2014年硕士论文

【摘要】：近年来,CDO发展迅速。如何进行CDO的风险评估,对其进行公平的价差评价,是促进其健康发展的重要因素。国内的学者和实务界的业内人士对相关领域的研究还涉足较少,很少对CDO的信用风险进行讨论分析,缺乏信用风险的评价体系。归根结底,还是未能对CDO产品进行准确合理的定价。深入分析CDO的合理定价,对促进我国金融改革有非常广阔的应用前景。本文分别基于t-NIG分布和G-NIG分布的单因子Copula模型在大样本同质投资组合(LHP)的近似情况下给出了两个CDO定价模型具体的定价步骤：计算CDO资产池资产的违约概率和损失分布；并通过CDO定价的半解析法,根据无套利思想,得到了CDO分券层价差的计算公式。最后,基于定价模型对信用衍生品指数Dow Jones iTraxx Europe指数2006年4月13日的各分券层定价进行了数值分析,分析对比了Dow Jones iTraxx Europe指数的市场价格和本文中几种单因子Copula定价模型的定价结果,发现了G-NIG Copula模型的定价结果最贴合市场报价,且单因子Copula模型中因子变量所服从的分布和模型中自由参数的数量是决定CDO定价与市场报价贴合程度的两个重要因素。更进一步,分别引入二状态(贝努利)随机相关系数和三状态(对称)随机相关系数,理论上对单因子Copula的CDO定价模型进行扩展。为定价模型的改进和应用提供理论和实证参考。
[Abstract]:CDO has developed rapidly in recent years. How to evaluate the risk of CDO and evaluate its fair spread is an important factor to promote its healthy development. Domestic scholars and practitioners are still involved in less research in related fields, rarely discuss and analyze the credit risk of CDO, and lack a credit risk evaluation system. After all, still fail to carry on accurate and reasonable price to CDO product. Further analysis of reasonable pricing of CDO has a very broad application prospect for promoting financial reform in China. In this paper, based on t-NIG distribution and G-NIG distribution, two specific pricing steps of CDO pricing model are given under the approximation of large sample homogeneous portfolio. The default probability and loss distribution of CDO asset pool are calculated. Based on the semi-analytic method of CDO pricing and the idea of no arbitrage, the formula for calculating the price difference of CDO coupon layer is obtained. Finally, based on the pricing model, the pricing of the credit derivative index Dow Jones iTraxx Europe on April 13, 2006, is analyzed numerically. This paper analyzes and compares the market price of Dow Jones iTraxx Europe index and the pricing results of several single factor Copula pricing models in this paper. It is found that the G-NIG Copula model is the most suitable for market price. The distribution of factor variables in single factor Copula model and the number of free parameters in the model are two important factors to determine the degree of matching between CDO pricing and market quotation. Furthermore, the two-state (Bernoulli) random correlation coefficient and the three-state (symmetric) stochastic correlation coefficient are introduced, respectively, to extend the CDO pricing model of single-factor Copula. To provide theoretical and empirical reference for the improvement and application of pricing model.
【学位授予单位】：浙江工业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91

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