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.

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.