本文選題：約化信用風(fēng)險模型 + 稀疏相關(guān)結(jié)構(gòu)��； 參考：《蘇州大學(xué)》2013年博士論文

【摘要】：自從2007年次貸危機(jī)發(fā)生以來,信用風(fēng)險的量化分析越來越受到人們的重視.約化信用風(fēng)險模型是一種重要的信用風(fēng)險度量模型.在約化信用風(fēng)險模型中,違約相關(guān)性的刻畫一直是人們建模的重點(diǎn).本論文在約化模型框架下,對違約相關(guān)結(jié)構(gòu)進(jìn)行建模,對違約風(fēng)險進(jìn)行了量化分析,并且對信用衍生品市場中最基礎(chǔ)最核心的產(chǎn)品進(jìn)行了定價. 目前,約化信用風(fēng)險模型按照違約相關(guān)性的刻畫的不同,主要分為以下四大類：傳染模型、因子copula模型、條件違約獨(dú)立模型、common shock模型.本論文提出了稀疏相關(guān)信用風(fēng)險模型和具有機(jī)制轉(zhuǎn)換(regime switching)的馬爾科夫copula模型,這兩個模型與common shock模型都有密切的關(guān)系. 本論文所建立的稀疏相關(guān)信用風(fēng)險模型在稀疏概率取得特殊值時,就是經(jīng)典的common shock模型,所以稀疏相關(guān)信用風(fēng)險模型是common shock模型的一種推廣.通過在模型中引入共同的經(jīng)濟(jì)狀態(tài)變量,建立起了具有機(jī)制轉(zhuǎn)換的稀疏相關(guān)信用風(fēng)險模型.首先考慮簡單的情形：強(qiáng)度過程隨著經(jīng)濟(jì)狀態(tài)的變化取不同的常數(shù)值,然后考慮強(qiáng)度過程是跳擴(kuò)散過程,而飄移系數(shù)和擴(kuò)散系數(shù)則隨著經(jīng)濟(jì)狀態(tài)的變化作相應(yīng)改變的情形.本論文通過計算多個公司的聯(lián)合生存(條件)概率,對模型中的違約風(fēng)險進(jìn)行了量化分析.作為模型的應(yīng)用,論文對一些交易最活躍的組合信用衍生品,比如一籃子信用違約互換(一籃子CDS),信用違約互換指數(shù)(CDX)以及抵押債務(wù)債券(CDO)進(jìn)行了定價. 與common shock模型類似,馬爾科夫copula模型的違約相關(guān)性是通過同時違約實(shí)現(xiàn)的.但是common shock模型側(cè)重刻畫違約事件,而馬爾科夫copula模型則側(cè)重刻畫違約指標(biāo)過程本身,因而兩個模型下,進(jìn)行違約風(fēng)險的量化分析的方法是完全不同的,后者主要用到鞅方法. 本論文把馬爾科夫copula模型應(yīng)用到具有雙邊對手風(fēng)險的信用違約互換(CDS)的定價問題中,并且用市場數(shù)據(jù)把模型中的參數(shù)估計出來,然后分析了參數(shù)的變化對互換率之差的影響.這里互換率之差是指具有雙邊對手風(fēng)險的CDS的互換率與具有單邊對手風(fēng)險的CDS的互換率之差. 進(jìn)一步,本論文還在馬爾科夫copula模型中引入共同的經(jīng)濟(jì)狀態(tài)變量,從而使得模型的違約相關(guān)性還受到經(jīng)濟(jì)環(huán)境因素的影響.論文證明了具有轉(zhuǎn)換機(jī)制的的馬爾科夫copula模型下的違約指標(biāo)過程仍具有鞅性質(zhì).論文最后對具有雙邊對手風(fēng)險的CDS進(jìn)行了定價,并且通過數(shù)值計算,考察了不同的經(jīng)濟(jì)環(huán)境對互換率的影響.
[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.
【學(xué)位授予單位】：蘇州大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：F830.5;F224;F830.91

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