Discrete time modeling of subprime mortgage credit

Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2011.

Many analysts believe that problems in the United States housing market initiated the 2007-2009 global financial crisis. In this regard, the subprime mortgage crisis (SMC) shook the foundations of the financial industry by causing the failure of many iconic Wall Street investment banks and prominent depository institutions. This crisis stymied credit extension to households and businesses thus creating credit crunches and, ultimately, a global recession. This thesis specifically discusses the SMC and its components, causes, consequences and cures in relation to subprime mortgage origination, data as well as bank bailouts. In particular, the SMC has highlighted the fact that risk, credit ratings, profit and valuation as well as capital regulation are important banking considerations. With regard to risk, the thesis discusses credit (including counterparty), market (including interest rate, basis, prepayment, liquidity and price), tranching (including maturity mismatch and synthetic), operational (including house appraisal, valuation and compensation) and systemic (including maturity transformation) risks. The thesis introduces the IDIOM hypothesis that postulates that the SMC was largely caused by the intricacy and design of subprime agents, mortgage origination that led to information problems (loss, symmetry and contagion), valuation opaqueness and ineffective risk mitigation. It also contains appropriate examples, discussions, timelines as well as appendices about the main results on the aforementioned topics. Numerous references point to the material not covered in the thesis, and indicate some avenues for further research. In the sequel, the banks that we study are subprime interbank lenders (SILs), subprime originators (SORs), subprime dealer banks (SDBs) and their special purpose vehicles (SPVs) such as Wall Street investment banks and their special structures as well as subprime investing banks (SIBs). Furthermore, the primary subprime agents that we consider are house appraisers (HAs), mortgage brokers (MBs), mortgagors (MRs), servicers (SRs), trustees, underwriters and credit enhancement providers (CEPs). Also, the insurers involved in the subprime market are originator mortgage insurers (OMIs) and monoline insurers (MLIs). The main components of the SMC are MRs, the housing market, SDBs/hedge funds/money market funds/SIBs, the economy as well as the government (G) and central banks. Here, G either plays a regulatory, bailout or policy making role. Most of the aforementioned banks and agents are assumed to be risk neutral with SOR being the exception since it can be risk (and regret) averse on occasion. The three main aspects of the SMC - subprime mortgage origination, data and bailouts - that we cover in this thesis and the chapters in which they are found are outlined below. In Chapter 2, we discuss the dynamics of SORs' capital, information, ratings, risk and valuation under mortgage origination. In particular, we model subprime mortgages that are able to fully amortize, voluntarily prepay or default and construct a discrete-time model for SOR risk and profit incorporating costs of funds and mortgage insurance as well as loan losses. Furthermore, a constrained optimal valuation problem for SORs under mortgage origination is solved. In addition, we show how high loan-to-value ratios curtailed the refinancing of subprime mortgages, while low ratios imply favorable house equity for subprime MRs. Chapter 2 also explores the relationship between Basel capital regulation and the SMC. This involves studying bank credit and capital under Basel regulation. Further issues dealt with are the quantity and pricing of subprime mortgages as well as credit ratings under Basel capital regulation. A key problem is whether Basel capital regulation exacerbated the SMC. Very importantly, the thesis answers this question in the affirmative. Chapter 3 contains subprime data not presented in Chapters 2. We present other mortgage data that also have connections with the main subprime issues raised. In Chapter 4, a troubled SOR's recapitalization by G via subprime bank bailouts is discussed. Our research supports the view that if SOR is about to fail, it will have an incentive not to extend low risk mortgages but rather high risk mortgages thus shifting risk onto its creditors. Here, for instance, we analyze the efficiency of purchasing toxic structured mortgage products from troubled SORs as opposed to buying preferred and common equity. In this regard, we compare the cases where SORs' on-balance sheet mortgages are fully amortizing, voluntarily prepaying (refinancing and equity extraction) and involuntarily prepaying (defaulting). If bailing out SORs considered to be too big to fail involves buying assets at above fair market values, then these SORs are encouraged ex-ante to invest in high risk mortgages and toxic structured mortgage products. Contrary to the policy employed by G, purchasing common (preferred) equity is always the most (least) ex-anteand ex-post-efficient type of capital injection. Our research confirms that this is true irrespective of whether SOR volunteers for recapitalization or not. In order to understand the key results in Chapters 2 to 4, a working knowledge of discrete-time stochastic modeling and optimization is required. The work presented in this thesis is based on a book (see [103]), 2 peer-reviewed international journal articles (see [51] and [105]), 2 peer-reviewed chapters in books (see [104] and [110]) and 4 peer-reviewed conference proceedings paper (see [23], [106], [107] and [109]).

Doctoral