几类信用衍生品定价问题的研究

发布时间：2018-02-02 16:31

本文关键词：仿射跳扩散过程自下而上的方法带移民的分支过程抵押债务凭证抵押债务凭证分券信用违约掉期信用风险对手风险信用溢价违约相关双随机 Poisson 过程动态对冲流动风险组合信用衍生品随机中心回归结构化模　出处：《南开大学》2012年博士论文　论文类型：学位论文

【摘要】：这篇博士论文研究了几个不确定条件下的衍生品定价问题.我们主要考虑了三类衍生品:第一类是组合信用衍生品(多标的信用衍生品),主要考虑抵押债务凭证(CDO)以及n次违约CDS;第二类是公司债券,公司债券可以看作是公司价值的信用衍生品;第三类是波动率互换,考虑了其最优动态对冲问题. 组合信用衍生品是近十年来迅速发展的一类信用衍生品,通常用来转移组合信用风险.与其它常见的信用衍生品(如信用违约掉期)相比,组合信用衍生品的标的资产是一个资产池,其现金流则取决于这个资产池中资产的损失(违约)情况.组合信用风险建模的困难是资产池中资产的数目太多,灵活的模型往往需要借助Monte Carlo模拟来进行衍生品定价和模型校准,时间花费巨大.本论文的第二章和第三章致力于建立计算简便又具有相应灵活性的组合信用风险模型,分别从自下而上和自上而下两个角度考虑了组合信用衍生品的定价问题. 第二章从自下而上的角度给出了两类组合信用风险.第一类利用[1]提出的模型,我们给出了一个计算组合信用衍生品的新方法,该方法在计算衍生品价格时不依赖于Fourier变换以及Fourier逆变换,也无需使用Monte Carlo模拟.我们的第二类模型不同于[1],但仍能利用仿射跳扩散过程以及双随机Poisson过程的信用风险模型,使得该模型易于计算.我们给出了公司债券,信用违约掉期以及组合信用衍生品的定价方法. 第三章从自上而下的角度考虑组合信用风险.我们首先利用带移民的离散时间分支过程对资产池中违约资产的个数进行建模,在违约回复率是常数的前提下得到了抵押债务凭证的定价方法.我们进行了数值试验来研究不同参数对价格的影响,结果表明我们的模型具有相应的灵活性,能够刻画市场价格的变动.此模型的缺点是违约资产的个数可能会远大过资产池中资产的总数.特别是当资产总数较少时定价可能会不准确.因此我们进一步提出了一个改进的模型,通过设立一个“对照资产池”,并对“对照资产池”中违约资产个数进行建模,解决了“原资产池”中违约资产个数可能远大过资产总数的问题. 在第四章,我们将注意力集中到流动性风险对公司债券价格的影响方面.通过结构化方法建立债券价格模型,并引入流动性风险,我们得到了公司债券价格的解析表达式.数值试验的结果表明在该模型下,公司债券短期的期限结构发生了变化,产生了风险溢价,从而解决了在一般的结构化模型中(比如[2])公司债券的短期风险溢价为零的问题. 在第五章,我们考虑波动率互换的对冲问题.假设标的资产的价格动态分别服从离散时间和连续时间下的平稳独立增量过程,我们得到了相应的动态最优对冲策略.我们以[3]中的跳扩散过程为例进行了数值试验,结果显示对冲误差达到了0.5%以内.
[Abstract]:This doctoral thesis studies the pricing of derivatives under several uncertain conditions. We mainly consider three types of derivatives: the first is portfolio credit derivatives (multi-subject credit derivatives). The main consideration is CDO (CDO) and default CDSs (n times); The second is corporate bonds, which can be regarded as credit derivatives of corporate value; The third is volatility swap, which considers its optimal dynamic hedging problem. Portfolio credit derivatives are a kind of credit derivatives developed rapidly in the past decade, which are usually used to transfer portfolio credit risk, compared with other common credit derivatives (such as credit default swaps). The underlying assets of portfolio credit derivatives are a pool of assets whose cash flow depends on the loss (default) of the assets in the pool. The difficulty of modeling portfolio credit risk is that there are too many assets in the pool of assets. Flexible models often require Monte Carlo simulations to price derivatives and calibrate models. The second and third chapters of this paper are devoted to the establishment of a simple and flexible portfolio credit risk model. The pricing of portfolio credit derivatives is considered from the bottom-up and top-down perspectives respectively. In the second chapter, two types of combination credit risk are given from the bottom-up perspective. [In the proposed model, we present a new method for calculating portfolio credit derivatives, which does not depend on Fourier transform and Fourier inverse transformation in calculating the price of derivatives. There is no need to use Monte Carlo simulation. Our second model is different from. [1], but the credit risk model of affine jump diffusion process and double stochastic Poisson process can still be used to make the model easy to calculate. We give the corporate bond. The pricing of credit default swaps and portfolio credit derivatives. In the third chapter, we consider portfolio credit risk from a top-down perspective. Firstly, we use the discrete time branching process with immigration to model the number of defaulted assets in the asset pool. Under the condition that default response rate is constant, the pricing method of CDOs is obtained. We have carried out numerical experiments to study the effect of different parameters on the price. The results show that our model has the corresponding flexibility. The disadvantage of this model is that the number of defaulted assets may be larger than the total number of assets in the asset pool. Especially when the total number of assets is small, pricing may not be accurate. An improved model has been developed. By setting up a "controlled asset pool" and modeling the number of defaulted assets in the "controlled asset pool", the problem that the number of defaulted assets in the "original asset pool" may exceed the total number of assets is solved. In Chapter 4th, we focus on the influence of liquidity risk on corporate bond price. Through structured approach, we establish bond price model and introduce liquidity risk. We obtain the analytical expression of the corporate bond price. The numerical results show that the short-term maturity structure of corporate bonds has changed under the model, resulting in a risk premium. Thus solving the problem in general structured models such as [(2) the problem of zero short-term risk premium for corporate bonds. In Chapter 5th, we consider the hedging problem of volatility swaps. We assume that the price dynamics of underlying assets are based on the stationary independent increment process of discrete time and continuous time respectively. We get the corresponding dynamic optimal hedging strategy. We use the [The numerical results show that the hedge error is less than 0.5%.
【学位授予单位】：南开大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：F830.9;F224

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