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.

Change of composition and diversity of species and grassland management between different grazing intensity in Pannonian dry and wet grasslands

Investigations were carried out in wet and dry pasture. Coenological recordings were taken in three zones. The first zone (“A”) located 0-50 m near the stable, second zone (“B”) located 50-150 m from the stable, while the third zone (“C”) located farther than 150 m. We have carried out analyses of ecological and environmental factors and life form types. Based on our results for both dry and wet grasslands, quadrates of “A” zone were well isolated from the rest of the zones. Overgrazing, which involves considerable trampling, vanishes differences among vegetations, thereby promotes weed and disturbance tolerant rich vegetation. The lowest species number and diversity could be found here. Due to the nitrogen enrichment due to the constant presence of livestock, drier and less heat demanding habitat developed in the “A” zones, according to the environmental indicators. Because of the change in management, conservation and diversity values of “C” zone increased, however, according to nature protection values it underperformed compared to “B” zone. According to the sample area, wet grasslands from the sandy areas of Kiskunság, preserve nature protection values and grass composition better moving away from stables, due to less grazing pressure. Drier backgrounds tolerate stronger grazing pressure.