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学博士后主要研究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。这类模型一般分为两类。在其中一种“结构形式”模型中，当一家公司的价值触及较低的障碍时，违约就会发生。这些措施直觉上很吸引人，但在它们纯粹的形式中，它们遭受了一个事实，即违约从来都不令人惊讶。第二类模型是那些“简化形式”的模型，它们假定了一个触发违约的外生事件。这些模型具有违约事件的到达强度，而这些模型的困难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，其中强度过程由两个因素驱动，一个在快时间尺度上演变，另一个在慢时间尺度上演变。随着FAST时间尺度接近无穷大，这类模型可以进行渐近分析。近年来的情况表明，金融债务违约是一种真实的可能性，因此，出现了许多提供某种形式违约保护的金融工具。这些工具是一种衍生证券。对于发行和交易这些工具的银行来说，为这些工具定价并管理与之相关的风险已成为一个关键问题。为此已经开发了许多数学模型，每个模型都有一定的缺陷。根据这笔拨款，主要研究人员和一名博士后研究员将基于一种已被证明对其他类型的衍生品证券建模有用的新方法，开发一类新的模型。

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.