Recent years see more and more importance of the management of credit risk for investors, especially institutional investors having large portfolio of corporate bonds, loans or other credit products. Questions like how to evaluate the credit value-at-risk given large amount of information (like different ratings and multiple credit metrics issued by different rating companies), how to build an efficient credit portfolio (having the highest expected return under certain level of credit risk) become increasingly difficult to solve using traditional methods and models. Especially for the second question, the rising dimension of the portfolio under limited computational speed call for leveraging some more robust algorithms for the large portfolio optimization.
In this paper, we will choose JP Morgan’s credit metrics model to evaluate the portfolio’s credit value-at-risk for the elaboration of our thesis and try to solve the problem of how to leverage multiple credit metrics (as a major input for the model) issued by different rating firms to largely reduce the negative impact of variation of different sources, for the slightest difference among the metrics might result in a huge deviation in the evaluation of the credit risk. At last we will introduce and exploit an increasingly popular and robust algorithm in today’s Large Scale Linear Planning Problem---Simulated Annealing to optimize our credit portfolio.
In contemporary market, people prefer to products with best quality at the lowest prices, regardless of where they are produced. Hence, most companies can no longer afford to produce their products in a single plant to provide the products needed with the lowest production cost in the market [5]. To get the edge of competitive strategy, several studies ([9], [20], [37]) suggest that firms should transfer production to locations for lowing production cost and maximizing total production quantities in a whole while maintaining quality and reliability.
The term production is typically used to denote the process of transforming input resources into output products. The allocation problem of input resources such that the output is maximized has been a critical issue since early 1900. The neoclassical authors around early 1900 used production function to relate outputs to its underlying input factors to manifest production-related phenomena such as diminishing returns [26], [34]. Although Wicksell contributed the initiative work of production function ([14], [26], [31], [36]), the term Cobb-Douglas function stands for production function in honor of Cobb and Douglas’ articles published in the American Economic Review ([8]).
Mortgage-backed securities market has recently become the largest capital market for investors in the U.S. Not surprisingly, a large volume of literature studies mortgage borrowers’ prepayment and default behavior and its impact on the pricing of mortgage backed securities. However, due to errors in variables or limited availability of borrower characteristics, most empirical studies find a substantial discrepancy between the theoretically derived optimal behavior and the observed decisions. (See, for example, Deng, Quigley and Van Order [1996] and Stanton [1996]). This paper attempts to reconcile the theoretical option-based models of mortgage terminations with the empirical experience of mortgage terminations by refinancing, sale and default.
From a theoretical perspective, we explicitly model the borrower’s costs associated with mortgage terminations and recognize that those costs vary across individuals and termination causes. Consistent with this approach, we empirically separate the three major causes of mortgage termination: refinancing, selling of the property, and default. Furthermore, since borrowers of similar characteristics (education, income, culture and ethnic background, etc.) tend to cluster together in neighborhoods, many of the omitted variables and measurement errors are spatially correlated. Recognizing this spatial correlation we empirically model the variability of the mortgage termination costs through the use of the physical location of the properties. This approach gives raise to a competing risks hazard framework with spatially correlated errors.
