Large Investor Analysis and Equilibrium Problems for Mortgage Backed Securities

这位调查员和他的同事研究复杂金融工具中的大型投资者。此外，他还考虑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进传统的抵押贷款合同。对于大型投资者分析，研究者试图回答一个基本问题，即当合约本身带有固有风险时，金融机构为什么会在衍生品合约中持有大量头寸。投资者和基础市场的什么因素会诱发这种行为？投资者能否找到一个愿意与之交易的对手方？为什么？持有大量头寸所产生的反馈效应是什么？对于抵押贷款支持证券的分析，研究者表明，目前的数学模型可以确定公平的抵押贷款发起率。由于这些利率通常是使用临时方法计算的，因此分析既可以更深入地了解这些利率对更广泛经济因素的敏感性，又可以作为预测未来利率的宝贵工具。最后，研究者研究了最近关于调整传统抵押贷款合同的建议，以减轻买家在房价下跌时选择性违约贷款的“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，但缺乏严格的证据来证明给定方法的可行性或优越性。这样的证明将有助于确定应该将哪个提案引入市场。研究生也参与了该项目的工作。研究者使用随机分析的现代工具来了解衍生品市场中的大型投资者。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急性敏感性，并且在对冲错误消失的渐近完全设置中，大投资者被视为内生的。他开发了新的大偏差结果，并运用了不完全市场中的最优投资和均衡理论，展示了大仓位是如何产生的，并描述了由此产生的均衡。最后，由于大仓位可能会引起反馈效应，如价格影响，研究者研究这些影响是否如此严重，以至于首先排除了大投资者的存在。对于抵押贷款支持证券分析，研究者使用现代功能分析来证明机构支持的住房抵押贷款池的公平抵押贷款利率的存在，同时考虑到提前支付和违约。此外，他还利用连续时间最优停止理论和偏微分方程来研究传统抵押合同的拟议变化。我们的目标是要证明，在房价下跌的情况下，这些变化是否有效地降低了房主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.