Intenzitásalapú modellezés és a mértékcsere (Intensity-based modeling and thje change of measure)

A dolgozatban a hitelderivatívák intenzitásalapú modellezésének néhány kérdését vizsgáljuk meg. Megmutatjuk, hogy alkalmas mértékcserével nemcsak a duplán sztochasztikus folyamatok, hanem tetszőleges intenzitással rendelkező pontfolyamat esetén is kiszámolható az összetett kár- és csődfolyamat eloszlásának Laplace-transzformáltja. _____ The paper addresses questions concerning the use of intensity based modeling in the pricing of credit derivatives. As the specification of the distribution of the lossprocess is a non-trivial exercise, the well-know technique for this task utilizes the inversion of the Laplace-transform. A popular choice for the model is the class of doubly stochastic processes given that their Laplace-transforms can be determined easily. Unfortunately these processes lack several key features supported by the empirical observations, e.g. they cannot replicate the self-exciting nature of defaults. The aim of the paper is to show that by using an appropriate change of measure the Laplace-transform can be calculated not only for a doubly stochastic process, but for an arbitrary point process with intensity as well. To support the application of the technique, we investigate the e®ect of the change of measure on the stochastic nature of the underlying process.

Modeling the Impacts of Climate Change on Phytogeographical Units. A Case Study of the Moesz Line

Regional climate models (RCMs) provide reliable climatic predictions for the next 90 years with high horizontal and temporal resolution. In the 21st century northward latitudinal and upward altitudinal shift of the distribution of plant species and phytogeographical units is expected. It is discussed how the modeling of phytogeographical unit can be reduced to modeling plant distributions. Predicted shift of the Moesz line is studied as case study (with three different modeling approaches) using 36 parameters of REMO regional climate data-set, ArcGIS geographic information software, and periods of 1961-1990 (reference period), 2011-2040, and 2041-2070. The disadvantages of this relatively simple climate envelope modeling (CEM) approach are then discussed and several ways of model improvement are suggested. Some statistical and artificial intelligence (AI) methods (logistic regression, cluster analysis and other clustering methods, decision tree, evolutionary algorithm, artificial neural network) are able to provide development of the model. Among them artificial neural networks (ANN) seems to be the most suitable algorithm for this purpose, which provides a black box method for distribution modeling.

Comparative Assessment of Climate Change Scenarios Based on Aquatic Food Web Modeling

In the years 2004 and 2005, we collected samples of phytoplankton, zooplankton, and macroinvertebrates in an artificial small pond in Budapest (Hungary). We set up a simulation model predicting the abundances of the cyclopoids, Eudiaptomus zachariasi, and Ischnura pumilio by considering only temperature and the abundance of population of the previous day. Phytoplankton abundance was simulated by considering not only temperature but the abundances of the three mentioned groups. When we ran the model with the data series of internationally accepted climate change scenarios, the different outcomes were discussed. Comparative assessment of the alternative climate change scenarios was also carried out with statistical methods.

Modeling the future distribution of Mediterranean Pinus species

The potential future distribution of four Mediterranean pines was aimed to be modeled supported by EUFORGEN digital area database (distribution maps), ESRI ArcGIS 10 software’s Spatial Analyst module (modeling environment), PAST (calibration of the model with statistical method), and REMO regional climate model (climatic data). The studied species were Pinus brutia, Pinus halepensis, Pinus pinaster, and Pinus pinea. The climate data were available in a 25 km resolution grid for the reference period (1961-90) and two future periods (2011-40, 2041-70). The climate model was based on the IPCC SRES A1B scenario. The model results show explicit shift of the distributions to the north in case of three of the four studied species. The future (2041-70) climate of Western Hungary seems to be suitable for Pinus pinaster.