Large Investor Analysis and Equilibrium Problems for Mortgage Backed Securities

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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.