信用违约互换的定价与模型

发布时间：2018-01-12 11:03

本文关键词：信用违约互换的定价与模型　出处：《山东大学》2013年硕士论文　论文类型：学位论文

【摘要】：现代金融市场两个重要的发展是资产的证券化和衍生产品的大量使用,而信用衍生品正是这两者的合理延伸。随着金融体制改革,金融竞争将更加激烈,金融风险更加突出,迫切需要引入新的信用风险管理方法和技术。信用衍生品是20世纪90年代末发展起来的一种用于规避信用风险的新型金融衍生工具。因此研究信用衍生品的定价问题日渐迫切。本文主要讲述了信用违约互换的定价和模型。信用违约互换包括单一公司的信用违约互换和一篮子信用违约互换两部分。在单一公司的信用违约互换的定价与模型中,首先假定债券发行公司的生存概率已知的情况下，，利用无套利原理计算出了信用违约互换的价格。其次,在根据结构化方法的基础上,通过求解几何布朗运动得到生存概率的表达式,并用Monte Carlo方法模拟出标准布朗运动,进而求出生存概率。最后,CDS定价模型计算了一个具体的例子,并分析了CDS的到期时间、期望回收率以及公司的波动率和CDS价格之间的关系。一篮子信用违约互换又分为首次信用违约互换和第N次信用违约互换。该部分利用单因子t-Copula模型,并用Beta分布、正态分布、对数正态分布以及二项分布模拟随机回收率进行定价,并探讨随机回收率在服从以上四种分布时的信用价差的变化。模拟结果发现,随着违约的次数的增加,无论是固定回收率还是各种分配下的随机回收率,其合理的信用价差都逐渐降低。因为随着违约次数的增加,累积发生的概率越低,则期望损失的现值会降低,因此信用价差随着降低。各种分配下的随机回收率所得的信用价差与固定回收率得到的信用价差相比较,固定回收率的信用价差要高于所有随机回收率的信用价差,故若使用固定回收率定价第N次信用违约互换将造成高估信用价差的情景。最后,重点考虑各种分配下的随机回收率模型重要参数的敏感度分析,这些重要参数主要包括风险率h、发行时间T、自由度v、相关系数ρ、回收率的样本均值μ、回收率的样本标准差σ等。在这些重要参数敏感度方面,模拟结果发现,随着风险率、到期时间的增加,信用价差也会发生同向变动；但随着相关系数、样本均值和自由度的增加,信用价差则会发生反向变动；而样本标准差的变化对信用价差没有明显影响。
[Abstract]:The two important developments of the modern financial market are the securitization of assets and the extensive use of derivative products, and credit derivatives are the reasonable extension of both. With the reform of the financial system, the financial competition will become more intense. Financial risk is more prominent. There is an urgent need to introduce new methods and techniques for credit risk management. Credit derivatives are a new type of financial derivatives developed at the end of 1990s to avoid credit risk. The issue of pricing is becoming increasingly urgent. This paper mainly describes the pricing and model of credit default swaps. Credit default swaps include credit default swaps of a single company and a basket of credit default swaps. In the model. First, assuming the survival probability of the bond issuing company is known, the price of credit default swaps is calculated by using the no-arbitrage principle. Secondly, based on the structured method. The expression of survival probability is obtained by solving geometric Brownian motion, and the standard Brownian motion is simulated by Monte Carlo method. Finally, the survival probability is obtained. The CDS pricing model calculates a concrete example, and analyzes the relationship between the expiration time of CDS, the expected recovery rate, the volatility of the company and the CDS price. A basket of credit default swaps is divided into first credit default swaps and N times credit default swaps. This part uses single factor t-Copula model and Beta distribution, normal distribution. The lognormal distribution and binomial distribution are used to simulate the random recovery rate and the variation of the credit spread between the four distributions is discussed. The simulation results show that with the increase of default times, whether the fixed recovery rate or the random recovery rate under various allocations, the reasonable credit spreads are gradually reduced, because with the increase of the number of defaults. The lower the probability of cumulative occurrence, the lower the present value of the expected loss, so the credit spread decreases. The credit spread of the fixed recovery rate is higher than that of all the random recovery rates, so if the fixed recovery rate is used to price the N times credit default swap, the situation of overestimating the credit spread will be caused. Finally, we focus on the sensitivity analysis of the important parameters of the stochastic recovery model under various distributions. These important parameters mainly include risk rate h, issue time T, degree of freedom v, correlation coefficient 蟻. The sample average of recovery is 渭, the sample standard deviation of recovery is 蟽, and so on. In the sensitivity of these important parameters, the simulation results show that with the increase of risk rate and expiration time, the credit spread will change in the same direction. However, with the increase of correlation coefficient, sample mean and degree of freedom, the credit spread will change inversely. However, the variation of sample standard deviation has no obvious effect on credit spread.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.9

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