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Application of perturbation methods to modeling correlated defaults in financial markets.

机译：扰动方法在金融市场相关违约建模中的应用。

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摘要

In recent years people have seen a rapidly growing market for credit derivatives. Among these traded credit derivatives, a growing interest has been shown on multi-name credit derivatives, whose underlying assets are a pool of defaultable securities. For a multi-name credit derivative, the key is the default dependency structure among the underlying portfolio of reference entities, instead of the individual term structure of default probabilities for each single reference entity as in the case of single-name derivative. So far, however, default dependency modeling is still the most demanding open problem in the pricing of credit derivatives. The research in this dissertation is trying to model the default dependency with aid of perturbation method, which was first proposed by Fouque, Papanicolaou and Sircar (2000) as a powerful tool to pricing options under stochastic volatility. Specifically, after a theoretic result regarding the approximation accuracy of the perturbation method and an application of this method to pricing American options under stochastic volatility by Monte Carlo approach, a multi-dimensional Merton model under stochastic volatility is studied first, and then the multi-dimensional generalization of the first-passage model under stochastic volatility comes next, which is then followed by a copula perturbed from the standard Gaussian copula.
机译：近年来，人们看到了信用衍生产品的快速增长的市场。在这些交易的信用衍生产品中，人们对多名称信用衍生产品的兴趣日益浓厚，其基础资产是可违约证券库。对于多名称信用衍生产品，键是参考实体的基础投资组合之间的默认依赖关系结构，而不是像单名称衍生产品那样，每个单个参考实体的默认概率的单独期限结构。但是，到目前为止，违约依存模型仍然是信用衍生产品定价中最苛刻的开放问题。本文的研究试图通过扰动方法对违约依赖进行建模，Fouque，Papanicolaou和Sircar（2000）首次提出，它是随机波动下定价期权的有力工具。具体而言，在获得有关摄动法近似精度的理论结果并将该方法应用于随机波动率下的蒙特卡罗方法对美式期权定价后，首先研究了随机波动率下的多维Merton模型，然后研究了多维接下来是随机波动下的首过模型的维数概括，然后是标准高斯copula扰动的copula。

著录项

  • 作者

    Zhou, Xianwen.;

  • 作者单位

    North Carolina State University.;

  • 授予单位 North Carolina State University.;
  • 学科 Mathematics.;Economics Finance.
  • 学位 Ph.D.
  • 年度 2006
  • 页码 152 p.
  • 总页数 152
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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