一些信用衍生品的定价

发布时间：2018-06-27 04:46

本文选题：信用敞口期权 + 信用违约互换　；参考：《上海交通大学》2012年硕士论文

【摘要】：信用衍生品是这样的一种合约,它们的清算价取决于合约标的资产的信用价值。合约的标的资产一般为公司债券。最普遍的信用衍生品有两种：信用违约互换和信用敞口期权。金融机构对信用衍生品有着十分浓厚的兴趣,但信用衍生品的发展却很缓慢。这主要是因为,到目前为止仅有为数不多的数学模型能够对信用衍生品合约定价,且各有优劣。本篇文章的主要目的就是研究如何更好地为信用衍生品定价。文章开头介绍信用敞口期权的定义和一些相关性质。接着简单介绍了为信用衍生品定价的三类模型,分别是结构化模型(structural models),简化模型(reduced form models)和敞口模型(spread model)。文章的重点放在简化模型中的Das-Sundaram模型上,介绍了Das-Sundaram模型引入的远期无风险利率和远期敞口所遵循的随机过程,随机过程中无风险中性漂移项的导出和债券价格的递归形式。接着在历史数据的基础上,利用逐步回归、最小二乘回归等方法得出了随机变量SX_1,X_2S的相关系数,违约率,累计违约率和恢复率的表达形式和参数值。最后模拟了一些数据,并利用Matlab编程解决了Das-Sundaram模型在欧式、美式信用敞口期权,欧式路径依赖期权和信用违约互换上的应用。
[Abstract]:Credit derivatives are contracts whose liquidation prices depend on the credit value of the underlying asset. The underlying assets of the contract are generally corporate bonds. There are two most common credit derivatives: credit default swaps and credit exposure options. Financial institutions have a strong interest in credit derivatives, but the development of credit derivatives is slow. This is largely because so far only a handful of mathematical models have been able to price credit derivatives contracts and each has its advantages and disadvantages. The main purpose of this article is to study how to better price credit derivatives. At the beginning of the article, the definition of credit exposure option and some related properties are introduced. Then three kinds of models for pricing credit derivatives are briefly introduced, namely structured model (structural models), simplified model (reduced form models) and open model (spread model). This paper focuses on the Das-Sundaram model in the simplified model, and introduces the stochastic process of the forward risk-free interest rate and the forward exposure, the derivation of the risk-free neutral drift term in the stochastic process and the recursive form of the bond price introduced by the Das-Sundaram model. On the basis of historical data, the correlation coefficient, default rate, cumulative default rate and recovery rate of the random variable SX _ S _ 1X _ 2S are obtained by using the methods of stepwise regression and least square regression. Finally, some data are simulated, and the application of Das-Sundaram model in European type, American credit exposure option, European path dependent option and credit default swap is solved by Matlab programming.
【学位授予单位】：上海交通大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

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