一类约化信用风险模型的风险分析及应用

发布时间：2018-04-18 15:35

本文选题：约化信用风险模型 + 稀疏相关结构　；参考：《苏州大学》2013年博士论文

【摘要】：自从2007年次贷危机发生以来,信用风险的量化分析越来越受到人们的重视.约化信用风险模型是一种重要的信用风险度量模型.在约化信用风险模型中,违约相关性的刻画一直是人们建模的重点.本论文在约化模型框架下,对违约相关结构进行建模,对违约风险进行了量化分析,并且对信用衍生品市场中最基础最核心的产品进行了定价. 目前,约化信用风险模型按照违约相关性的刻画的不同,主要分为以下四大类：传染模型、因子copula模型、条件违约独立模型、common shock模型.本论文提出了稀疏相关信用风险模型和具有机制转换(regime switching)的马尔科夫copula模型,这两个模型与common shock模型都有密切的关系. 本论文所建立的稀疏相关信用风险模型在稀疏概率取得特殊值时,就是经典的common shock模型,所以稀疏相关信用风险模型是common shock模型的一种推广.通过在模型中引入共同的经济状态变量,建立起了具有机制转换的稀疏相关信用风险模型.首先考虑简单的情形：强度过程随着经济状态的变化取不同的常数值,然后考虑强度过程是跳扩散过程,而飘移系数和扩散系数则随着经济状态的变化作相应改变的情形.本论文通过计算多个公司的联合生存(条件)概率,对模型中的违约风险进行了量化分析.作为模型的应用,论文对一些交易最活跃的组合信用衍生品,比如一篮子信用违约互换(一篮子CDS),信用违约互换指数(CDX)以及抵押债务债券(CDO)进行了定价. 与common shock模型类似,马尔科夫copula模型的违约相关性是通过同时违约实现的.但是common shock模型侧重刻画违约事件,而马尔科夫copula模型则侧重刻画违约指标过程本身,因而两个模型下,进行违约风险的量化分析的方法是完全不同的,后者主要用到鞅方法. 本论文把马尔科夫copula模型应用到具有双边对手风险的信用违约互换(CDS)的定价问题中,并且用市场数据把模型中的参数估计出来,然后分析了参数的变化对互换率之差的影响.这里互换率之差是指具有双边对手风险的CDS的互换率与具有单边对手风险的CDS的互换率之差. 进一步,本论文还在马尔科夫copula模型中引入共同的经济状态变量,从而使得模型的违约相关性还受到经济环境因素的影响.论文证明了具有转换机制的的马尔科夫copula模型下的违约指标过程仍具有鞅性质.论文最后对具有双边对手风险的CDS进行了定价,并且通过数值计算,考察了不同的经济环境对互换率的影响.
[Abstract]:Since the subprime mortgage crisis occurred in 2007, people pay more and more attention to the quantitative analysis of credit risk.Reduced credit risk model is an important credit risk measurement model.In the reduced credit risk model, the description of default correlation has been the focus of modeling.Under the framework of reductive model, this paper models the default related structure, analyzes the default risk quantitatively, and pricing the most basic and core products in the credit derivatives market.At present, reduced-credit risk models are divided into the following four categories according to the different characterizations of default correlation: contagion model, factor copula model, conditional default independent model and common shock model.In this paper, a sparse correlation credit risk model and a Markov copula model with mechanism transformation are proposed. The two models are closely related to the common shock model.The sparse correlation credit risk model established in this paper is the classical common shock model when the sparse probability obtains the special value, so the sparse correlation credit risk model is a generalization of the common shock model.By introducing common economic state variables into the model, a sparse correlation credit risk model with mechanism transformation is established.The simple case is considered first: the intensity process takes different constant values with the change of the economic state, and then considers that the intensity process is a jump diffusion process, while the drift coefficient and diffusion coefficient change accordingly with the change of the economic state.In this paper, the risk of default in the model is analyzed quantitatively by calculating the joint survival (conditional) probability of multiple companies.As an application of the model, some of the most traded portfolio credit derivatives are priced, such as a basket of credit default swaps (CDSs), the credit default swap index (CDX) and mortgage-backed debt obligations (CDOs).Similar to common shock model, Markov copula model is implemented by simultaneous default.However, common shock model focuses on describing default events, while Markov copula model focuses on describing default index process itself. Therefore, the methods of quantitative analysis of default risk are completely different under the two models, the latter mainly using martingale method.In this paper, Markov copula model is applied to the pricing problem of credit default swaps (CDSs) with the risk of bilateral counterparty, and the parameters in the model are estimated by market data, and then the effect of the variation of parameters on the difference of swap rate is analyzed.The difference in swap rate is the difference between the swap rate of CDS with bilateral counterparty risk and the swap rate of CDS with unilateral counterparty risk.Furthermore, this paper also introduces common economic state variables into Markov copula model, which makes the default correlation of the model also affected by economic environmental factors.In this paper, we prove that the default index process of Markov copula model with transformation mechanism still has martingale properties.At the end of the paper, the CDS with bilateral counterparty risk is priced, and the effect of different economic environment on the swap rate is investigated by numerical calculation.
【学位授予单位】：苏州大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：F830.5;F224;F830.91

【相似文献】