GOALI: Carnegie Mellon - Morgan Stanley Mathematical Finance Postdoctoral Fellow

目标：卡内基梅隆-摩根士丹利数学金融博士后研究员主要研究人员将与一名博士后研究员一起参与公司债券违约模型的开发。 有两个这样的模型一般类。 在其中一个“结构形式”模型中，违约发生在公司价值触及较低障碍时。 直觉上，这些都很吸引人，但在纯粹的形式上，它们受制于这样一个事实，即违约从来都不是一个意外。 第二类模型，即“简化形式”模型，假定触发违约的外生事件。 这些模型具有违约事件到达的强度，这些模型的难点在于构建这种强度过程，以便模型符合市场数据。 这项工作将研究模型的行为，其中强度过程是由两个因素驱动的，一个在快速的时间尺度上发展，另一个在缓慢的时间尺度上。 这种模型在快时间尺度接近无穷大时，可以进行渐近分析。近年来，金融债务违约的可能性确实存在，因此，出现了许多提供某种形式的违约保护的金融工具。 这些工具是一种衍生证券。 为这些工具定价并管理与之相关的风险已成为发行和交易这些工具的银行的关键问题。 为此目的已经开发了许多数学模型，并且它们中的每一个都具有某些缺点。 根据这项资助，主要研究人员和一名博士后研究员将基于一种新方法开发一类新的模型，该方法已被证明在其他类型的衍生证券建模中很有用。

GOALI: Carnegie Mellon - Morgan Stanley Mathematical Finance Post-Doctoral FellowThe principal investigators will participate with a post-doctoral fellow on the development of models for corporate bond default. There are two general classes of such models. In one of these, the models of "structural form," default occurs when the value of a firm hits a lower barrier. These are intuitively appealing, but in their pure form they suffer from the fact that default is never a surprise. The second class of models, those of "reduced form," postulate an exogenous event which triggers default. These have an intensity of arrival of the default event, and the difficulty with these models is constructing this intensity process so that the model conforms to market data. This work will investigate the behavior of models in which the intensity process is driven by two factors, one evolving on a fast time scale and the other on a slow time scale. Such models are amenable to asymptotic analysis as the fast time scale approaches infinity.Recent years have shown that default on financial obligations is a genuine possibility, and as a result, many financial instruments which offer some form of protection against default have arisen. These instruments are a type of derivative security. Pricing these instruments and managing the risk associated with them has become a critical issue for the banks that issue and trade them. A number of mathematical models have been developed for this purpose, and each of them has certain drawbacks. Under this grant, the principal investigators and a post-doctoral fellow will develop a new class of models based on a novel approach that has proved useful in modeling other types of derivative securities.