Large Investor Analysis and Equilibrium Problems for Mortgage Backed Securities

这位研究人员和他的同事们研究了复杂金融工具的大投资者。此外，他还研究了抵押贷款支持证券市场，重点关注如何确定公平的抵押贷款利率，以及如何通过考虑房价下跌的负面影响来改善传统的抵押贷款合同。对于大型投资者的分析，调查者试图回答一个基本问题，即当衍生品合同本身带有内在风险时，为什么金融机构会在衍生品合同中持有大量头寸。投资者和基础市场会导致这种行为吗？投资者能找到愿意与之交易的交易对手吗？为什么？持有大量头寸会产生怎样的反馈效应？对于抵押贷款支持证券的分析，研究人员表明，目前的数学模型可以确定公平的抵押贷款发放率。由于这些利率通常是使用特别方法计算的，因此该分析既提供了对此类利率对更广泛经济因素的敏感性的更深层次的理解，也提供了预测未来利率的宝贵工具。最后，调查人员研究了最近关于调整传统抵押贷款合同的提议，以减轻购房者在房价下跌时选择性拖欠贷款的“水下”效应。这种违约给贷款机构和整体经济带来了巨大的成本。虽然已经提出了各种机制，但缺乏证明某一方法的可行性或优越性的严格证据。这样的证据将有助于确定哪一项建议应该引入市场。研究生都参与了这个项目的工作。调查人员使用随机分析中的现代工具来了解衍生品市场上的大投资者。特别是，大偏差理论是合适的，因为当对冲策略失败时，大投资者对罕见事件具有强烈的敏感性，而且大投资者被认为是在对冲错误消失的渐近完备环境中内生出现的。他发展了新的大偏差结果，并利用最优投资理论和不完全市场中的均衡理论，展示了大量头寸是如何产生的，并描述了由此产生的均衡。最后，由于大额仓位可能会导致价格影响等反馈效应，研究者研究这些效应是否严重到首先排除了大投资者的存在。对于抵押贷款支持的证券分析，调查者使用现代泛函分析来证明机构支持的住房抵押贷款池存在公平的抵押贷款利率，同时考虑了提前还款和违约。此外，他使用连续时间最优停止理论和偏微分方程来研究对传统抵押贷款合同的拟议变化。这样做的目的是表明，这些变化是否有效地降低了房主在房价下跌时选择性拖欠贷款的动机。

The investigator and his colleagues study large investors in complex financial instruments. Additionally, he considers the market for mortgage-backed securities, focusing on both how fair mortgage rates are determined, and how to improve the traditional mortgage contract by taking into account the negative effects of house price decline. For the large investor analysis, the investigator seeks to answer the basic question of why a financial institution would take a large position in a derivative contract when the contract itself carries inherent risks. What about the investor and underlying market would induce such behavior? Could the investor find a willing counter-party to transact with and why? What are the feedback effects which arise from taking a large position? For the mortgage-backed security analysis, the investigator shows that current mathematical models can determine fair mortgage origination rates. As these rates are typically computed using ad-hoc methods, the analysis provides both a deeper understanding of the sensitivities of such rates on broader economic factors, and a valuable tool for predicting future rates. Lastly, the investigator studies recent proposals for adjusting the traditional mortgage contract to mitigate the "underwater" effect of buyers selectively defaulting on their loans in the event of house price decline. Such defaults impose significant costs on the lending institutions as well as the broader economy. Though various mechanisms have been suggested, rigorous proofs showing the viability, or superiority, of a given method are lacking. Such proofs will help identify which proposal should be introduced into the marketplace. Graduate students are involved in the work of the project. The investigator uses modern tools from stochastic analysis to understand large investors in derivatives markets. In particular, the theory of large deviations is appropriate, as large investors have acute sensitivities to rare events when hedging strategies fail, and large investors are seen to arise endogenously in the asymptotically complete setting where hedging errors vanish. Developing new large deviations results, as well as using theories of optimal investment and equilibrium in incomplete markets, he shows how large positions arise and describes the resultant equilibrium. Lastly, since large positions may induce feedback effects such as price impact, the investigator studies whether these effects are so severe as to preclude the existence of large investors in the first place. For the mortgage-backed security analysis, the investigator uses modern functional analysis to prove existence of fair mortgage rates for agency-backed pools of residential mortgages, taking both prepayment and default into account. Additionally, he uses the theories of continuous time optimal stopping and partial differential equations to investigate proposed changes to the traditional mortgage contract. The goal is to show that these changes either do or do not effectively reduce the homeowner's incentive to selectively default on her loan in the event her house price has declined.