Analytical Solution for Expected Loss of a Collateralized Loan: A Square-root Intensity Process Negatively Correlated with Collateral Value

In this study, we derive an explicit solution for the expected loss of a collateralized loan, focusing on the negative correlation between default intensity and collateral value. Three requirements for the default intensity and the collateral value are imposed. First, the default event can happen at any time until loan maturity according to an exogenous stochastic process of default intensity. Second, default intensity and collateral value are negatively correlated. Third, the default intensity and collateral value are non-negative. To develop an explicit solution, we propose a square-root process for default intensity and an affine diffusion process for collateral value. Given these settings, we derive an explicit solution for the integrand of the expected recovery value within an extended affine model. From the derived solution, we find the expected recovery value is given by a Stieltjes integral with a measure-changed survival probability.stochastic recovery, default intensity model, affine diffusion, extended affine, survival probability, measure change

Analytical solutions for expected and unexpected losses with an additional loan

We evaluate expected and unexpected losses of a bank loan, taking into account the bankfs strategic control of the expected return on the loan. Assuming that the bank supplies an additional loan to minimize the expected loss of the total loan, we provide analytical formulations for expected and unexpected losses with bivariate normal distribution functions.There are two cases in which an additional loan decreases the expected loss: i) the asset/liability ratio of the firm is low but its expected growth rate is high; ii) the asset/liability ratio of the firm is high and the lending interest rate is high. With a given expected growth rate and given interest rates, the two cases are identified by two thresholds for the current asset/liability ratio. The bank maintains the current loan amount when the asset/liability ratio is between the two thresholds. Given the bankfs strategy, the bank decreases the initial expected loss of the loan. On the other hand, the bank has a greater risk of the unexpected loss.Probability of default (PD), Loss given default (LGD), Exposure at default (EaD), Expected loss (EL), Unexpected loss (UL), Stressed EL (SEL)

Analytical Solution for the Loss Distribution of a Collateralized Loan under a Quadratic Gaussian Default Intensity Process

In this study, we derive an analytical solution for expected loss and the higher moment of the discounted loss distribution for a collateralized loan. To ensure nonnegative values for intensity and interest rate, we assume a quadratic Gaussian process for default intensity and discount interest rate. Correlations among default intensity, discount interest rate, and collateral value are represented by correlations among Brownian motions driving the movement of the Gaussian state variables. Given these assumptions, the expected loss or the m-th moment of the loss distribution is obtained by a time integral of an exponential quadratic form of the state variables. The coefficients of the form are derived by solving ordinary differential equations. In particular, with no correlation between default intensity and discount interest rate, the coefficients have explicit closed form solutions. We show numerical examples to analyze the effects of the correlation between default intensity and collateral value on expected loss and the standard deviation of the loss distribution.default intensity, stochastic recovery, quadratic Gaussian, expected loss, measure change

GIS-based Forecast of Landscape Changes with the Ito Land Readjustment Project

The purpose of the present research is to attempt consolidation of geographic information into the GIS regarding the Ito Land Readjustment Project presently being implemented in northern Kyushu in Japan, and forecast the landscape changes before/after comparison of the project. First, the topographic map, 50-meter mesh digital map (elevation), aerial photograph, land use map, project plan, land use zone plan, district plan, substitute lot plan and other geographic information of the project district were collected from various sources and systematized. Thereafter the data were aggregated using ArcGIS. Next, building and structure data before and after the project were prepared and height data of these buildings and structures were combined with the land elevation data. Then, the major view point fields in the district were selected, to examine the extent of the change of the visibility areas from these view point fields before and after the project. Moreover, focusing on the mountains in the visibility areas, we forecasted how much the visibility area of the mountains would decrease at each view point field after construction of the buildings and structures in the project implementation. Finally, we showed 3-D images of the project district using ArcScene, and investigated the extent of visibility of the mountain range sky line from each view point field as before/after comparison of the project.

ChangeBeadsThreader: An Interactive Environment for Tailoring Automatically Untangled Changes

To improve the usability of a revision history, change untangling, which reconstructs the history to ensure that changes in each commit belong to one intentional task, is important. Although there are several untangling approaches based on the clustering of fine-grained editing operations of source code, they often produce unsuitable result for a developer, and manual tailoring of the result is necessary. In this paper, we propose ChangeBeadsThreader (CBT), an interactive environment for splitting and merging change clusters to support the manual tailoring of untangled changes. CBT provides two features: 1) a two-dimensional space where fine-grained change history is visualized to help users find the clusters to be merged and 2) an augmented diff view that enables users to confirm the consistency of the changes in a specific cluster for finding those to be split. These features allow users to easily tailor automatically untangled changes.Comment: 5 pages, SANER 202

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List of Polypores and Other Aphyllophoraceous Fungi Collected in the Lambir Hills National Park, Sarawak, Malaysia

We collected 933 specimens of polypores and other aphyllophoraceous fungi in the Lambir Hills National Park, Sarawak, Malaysia, in 2006. We identified 848 specimens and recorded 57 species and 59 morphospecies. We compare our list to the results of a few former floral studies conducted in and near the park