基于BDS和合成CDO的定价与对冲模型研究

发布时间：2018-01-05 10:28

本文关键词：基于BDS和合成CDO的定价与对冲模型研究　出处：《浙江大学》2013年博士论文　论文类型：学位论文

【摘要】：信用衍生品代表着过去二十多年来金融市场上最重要的创新,成为众多金融机构进行资产管理和风险管理所必不可少的工具。随着金融市场的发展以及市场风险的增加,深入研究信用衍生品特别是组合型产品的定价模型和对冲理论,构建出符合市场规律的数量模型是现实的需要,同时也对全球金融市场繁荣稳定的发展具有重大意义。本论文主要针对组合型信用衍生品中占据基础和核心地位的产品一篮子违约互换(BDS)和合成担保债责凭证(合成CDO)的定价和对冲进行研究,改进市场上现存的定价和对冲模型,期待为市场上的参与者能够更进一步了解信用衍生品,能够有效地进行风险管理和资产定价提供理论基础。在信用衍生品的定价方面,本论文针对市场上一般定价模型将回收率假设为确定的常数,违背市场回收率的变化规律,忽略回收风险,导致BDS定价及合成CDO分块特别是优先级分块定价失效等缺陷,在点随机回收率假设下,给出第一违约互换和第k违约互换的因子Copula定价模型及解析的定价公式。最后数值实验比较了在常回收率下和随机回收率下第一违约互换合约在齐次组合下的保费随资产池个数递增的变化情况,同时,数值实验还分析了保费随相关性参数变化的情况。实验结果反映了回收率的不同假设对定价结果产生重要影响,提醒市场上的参与者不能只注重违约风险,回收风险同样决定着投资者的收益。在信用衍生品的风险对冲方面,本文对产品BDS和合成CDO都进行了系统的研究。现如今市场上还缺乏一个理论性强且易操作的对冲模型。Laurent在2008年提出一个动态对冲CDO分块违约风险的策略模型。此模型基于鞅表示定理运用银行账户和组合型指数产品对CDO分块进行复制,并在一个动态组合树下实现了模型。本文基于此模型进行了改进和扩展,提出了一系列新的对冲策略模型。首先,本论文放松常回收率的假设,将回收率假设为资产池违约个数的线性函数并给出其校准程序,在此随机回收下,本文给出第一违约互换和第n违约互换的对冲策略模型。数值实验计算了第一违约互换和第n违约互换的对冲比例,并比较了在Laurent模型和本文所提模型下CDO分块[0,3%]和[12%,22%]的对冲比例结果。实验表明不同回收率对衍生品的对冲策略影响重大,特别是合成CDO的优先级分块。第二,本论文放松资产齐次组合假设,将资产池根据地域性及信用等级等特性分为两个齐次组,并假设每个组的强度依赖于两组的违约个数,在此基础上提出强度的校准程序并构建了第一违约互换和合成CDO分块的对冲策略模型。此模型为进一步建立更符合与市场实际的非齐次对冲策略模型提供了新的思路。最后,本论文针对市场上大多模型包括Laurent模型只考虑单一风险的对冲,忽略衍生品的信用加价风险和违约风险的同时存在性,而同时对冲这两种风险是今后信用衍生品风险对冲研究的重要问题,进而本论文首次引入组合预测思想建立了同时对冲CDO分块信用加价风险和违约风险的策略模型,并给出数值实验。此模型的构建为同时对冲两种风险的策略模型提供了新的方法。数量模型已成为市场定价和风险管理必备的工具,但是模型无论其多完善,都在一定程度上依赖于某种假设,违背市场的真实运行规律,有着不可避免的种种缺陷,因此进一步完善模型,最低程度依赖假设,揭示市场的真实规律是今后建模的关键,期待本文所提模型及相应的结果能为理论界和实务界对信用衍生品风险管理和资产定价提供思路。
[Abstract]:Credit derivatives represent the most important innovations in the financial markets over the past more than 20 years, a number of financial institutions are essential for asset management and risk management tool. With the increase of the development of the financial market and the market risk, especially in-depth study of credit derivatives pricing model and hedging theory combined products, build a quantitative model in line with the market the law is the realistic need, but also is of great significance to the development of global financial market stability and prosperity. This thesis focuses on the occupy the foundation and core combination of credit derivatives products in a basket default swap (BDS) and Synthetic Collateralized Debt and Liability Certificate (synthetic CDO) pricing and hedging of improved market the existing pricing and hedging models, looking for market participants to further understand the credit derivatives, can effectively carry out the wind Risk management and asset pricing provide a theoretical basis.
In the pricing of credit derivatives, the market will be a general pricing model to determine the recovery rate assumed constant, contrary to the changes of the market recovery, ignoring the recovery risk, resulting in BDS pricing and synthesis of CDO block in particular priority block pricing failure, the random recovery rate under the assumption that gives the first default swaps and the default K factor Copula pricing model and analytic swap pricing formula. Finally, numerical experiments on the recovery rate often changes, and random recovery rate of the first default swaps in homogeneous combinations of the premium with the number of asset pool increasing at the same time, the numerical experiments also analyzed the change of the premium with the correlation parameters. The experimental results show that the recovery rate of different assumptions have an important impact on the pricing results, remind the market participants can not only pay attention to the risk of default, recovery risk It also determines the returns of the investor.
In the credit derivatives to hedge risk, this paper has made a systematic study on the synthesis of CDO and BDS products. Now the market is the lack of a strong theoretical and operational hedge model of.Laurent proposed in 2008 a dynamic hedging strategy model of CDO block. The default risk model based on martingale representation theorem by the bank account and composite index products of CDO block copy, and implement the model in a dynamic combination tree. Based on this model was improved and extended, put forward a series of new hedge strategy model. Firstly, this paper put loose recovery often assumptions, the recovery rate is assumed for the calibration the program assetpool default number of linear function given in this random recovery, this paper gives the first to default swaps and the N default swaps hedge strategy model. The numerical experiment is calculated first to default swaps and the n. Swaps hedge ratio, and compares the Laurent model and the proposed model CDO block [0,3%] and [12%, the proportion of hedge results 22%]. The experimental results show that the recovery rate of different derivatives hedging strategies have significant impact, especially in the synthesis of CDO block priority. Second, this dissertation relaxes the homogeneous portfolio assets hypothesis. The asset pool is divided into two homogeneous groups according to the regional characteristics and credit rating, and assuming that each group is dependent on the strength of the two groups of the default number, based on the strength calibration procedure and constructed the first to default swaps and hedge strategy model of synthesis of CDO block. This model to further establish more in accordance with the inhomogeneous model and the actual market hedging strategy provides a new way of thinking. Finally, this thesis focuses on the market most models include the Laurent model only considers a single risk hedge, ignoring the credit derivatives price wind At the same time risks and there is a risk of default, while the two hedge risk is an important problem of risk hedging of credit derivatives in the future, then this paper first introduced the combination forecasting thought up the hedge CDO block increase credit risk and default risk model, and gives the numerical experiments. The construction of this model provides a new the methods and Strategies of model two and hedge risk.
The number of models have become the market pricing and risk management tools necessary, but regardless of how to improve the model, to a certain extent, rely on some assumptions, the real operation of violate the laws of the market, there are inevitable defects, so the further improvement of the model, the lowest degree depends on the true hypothesis, to reveal the rules of market is the key in future modeling look, the model proposed in this paper and the corresponding results for the theory and practice to provide ideas for credit derivatives risk management and asset pricing.

【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：F224;F830.9

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