In this brief research article, we consider the financial modelling of the process of mortgage loan securitization that has been a root cause of the ongoing Subprime Mortgage Crisis (SMC). In particular, we suggest a Levy process-driven model of bank leverage profit that arises from the securitization of a pool of subprime mortgage loans. To achieve this, we develop stochastic models for mortgage loans, mortgage loan losses, credit ratings and mortgage loan guarantees in a subprime context. These models incorporate some of the most important issues related to the SMC and its causes. Finally, we provide a brief analysis of the models developed earlier in our contribution and its relationship with the SMC.
The main categories of assets held by banks are loans, Treasuries (bonds issued by the national Treasury), reserves and intangible assets. In our contribution, we investigate the investment of bank funds in loans and Treasuries with the aim of generating an optimal final fund level. Our results take behavioral aspects such as risk and regret into account. More specifically, we apply a branch of optimization theory that enables us to consider a regret attribute alongside a risk component as an integral part of the utility function. In this case, regret-aversion corresponds to the convexity of the regret function and the bank's preference is assumed to be representable by optimization subject to the utility. In addition, we provide a comparison between risk-and regret-averse banks in terms of optimal asset allocation between loans and Treasuries. A feature of our contribution is that these and other optimization issues are analyzed briefly and, where possible, represented graphically. Furthermore, we comment on the claim that an investment away from loans towards Treasuries is responsible for credit crunches in the banking industry.
We analyze the process of mortgage loan securitization that has been a root cause of the current subprime mortgage crisis (SMC). In particular, we solve an optimal securitization problem for banks that has the cash outflow rate for financing a portfolio of mortgage-backed securities (MBSs) and the bank's investment in MBSs as controls. In our case, the associated Hamilton-Jacobi-Bellman equation (HJBE) has a smooth solution when the optimal controls are computed via a power utility function. Finally, we analyze this optimization problem and its connections with the SMC.
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