我们回顾了衡量流动性对CDS价格影响的不同方法。我们从简化形式的模型开始，将流动性作为一个额外的贴现率。我们回顾了Chen，Fabozzi and Sverdlove（2008）和Buhler and Trapp（2006，2008），对流动性利率如何进入CDS溢价率公式、流动性利率过程的动态以及信用流动性相关性采用了不同的假设。Buhler和Trapp（2008）提供了最普遍和最现实的框架，包括流动性和信用之间的相关性，债券和CDS合约之间的流动性溢出效应，以及CDS溢价率的非对称流动性效应。然后，我们讨论了Bongaerts，De Jong和Driessen（2009）的研究，该研究导出了一个包含流动性效应的均衡资产定价模型。研究结果包括，预期的非流动性和流动性风险对预期CDS回报有统计上的显着影响。最后，我们讨论了Predescu et al（2009），该研究也分析了危机中的数据。这是一个统计模型，将有序流动性得分与每个CDS参考实体相关联，并允许比较超过2400个参考实体的流动性。本研究指出，信用与流动性不足是相关的，并呈现微笑模式。所有这些研究都强调，CDS溢价率并不是信用风险的纯粹指标。需要进一步的研究来衡量CDS合约水平的流动性溢价，并有效地将流动性与信贷分离。
英文摘要：
We review different approaches for measuring the impact of liquidity on CDS prices. We start with reduced form models incorporating liquidity as an additional discount rate. We review Chen, Fabozzi and Sverdlove (2008) and Buhler and Trapp (2006, 2008), adopting different assumptions on how liquidity rates enter the CDS premium rate formula, about the dynamics of liquidity rate processes and about the credit-liquidity correlation. Buhler and Trapp (2008) provides the most general and realistic framework, incorporating correlation between liquidity and credit, liquidity spillover effects between bonds and CDS contracts and asymmetric liquidity effects on the Bid and Ask CDS premium rates. We then discuss the Bongaerts, De Jong and Driessen (2009) study which derives an equilibrium asset pricing model incorporating liquidity effects. Findings include that both expected illiquidity and liquidity risk have a statistically significant impact on expected CDS returns. We finalize our review with a discussion of Predescu et al (2009), which analyzes also data in-crisis. This is a statistical model that associates an ordinal liquidity score with each CDS reference entity and allows one to compare liquidity of over 2400 reference entities. This study points out that credit and illiquidity are correlated, with a smile pattern. All these studies highlight that CDS premium rates are not pure measures of credit risk. Further research is needed to measure liquidity premium at CDS contract level and to disentangle liquidity from credit effectively.
Completing CVA and Liquidity: Firm-Level Positions and Collateralized Trades
目前实施的双边CVA具有违反直觉的效果，即从自己不断扩大的CDS利差中获利，即在实践中增加违约风险。Morini & Prampolini（2010）提出的CVA和流动性的统一图景有助于理解这一点。然而，在实际执行中有两个重要的遗漏，它们来自同一来源，即在通常的头寸保持系统中没有登记的头寸。第一个遗漏是公司层面的头寸，这些头寸在公司违约时会改变价值。商誉就是一个例子，它是资产负债表上的一个项目，通常在违约时减记为零。另一个例子是公司股权。第二个遗漏涉及抵押头寸。当这些头寸在未来出现资金短缺时（这是一个积极的概率），它们将需要无法使用头寸本身获得的资金。这些或有未来融资头寸通常不会记入任何头寸保持系统。我们在这里展示如何包括这两种类型的头寸，从而帮助完成CVA和流动性的统一图景。对于一个特定的大型复杂的金融机构，在保守的假设下，盈利$2.5B from spread widening we show that including Goodwill would have resulted in a $ 4B损失。虽然我们不能对其抵押衍生品投资组合进行类似的评估，但我们计算了一系列掉期的融资成本和自身违约的CVA，并发现CVA在示例中是一个积极的贡献。
Valuation of Variable Annuities with Equity Protection Swaps under Jumps and Default Risks
School of Mathematics and Statistics, University of Sydney（悉尼大学数学与统计学院）；Faculty of Mathematics and Information Science, Warsaw University of Technology（华沙理工大学数学与信息科学学院）；National University of Singapore, Department of Mathematics（新加坡国立大学数学系）
