Válság és hitelderivatívák. A szintetikus fedezett adósságkötelezettségek (CDO-k) árazása és kockázataik (Crisis and loan derivatives. The pricing and risks of synthetic collateralized debt obligations)

A dolgozat első részében röviden áttekintjük a 2007-ben kezdődött pénzügyi válság lefolyását és a válsághoz vezető okokat. A bemutatás során igyekszünk végig a mögöttes folyamatokra és azok mozgatórugóira koncentrálni, ezzel megragadva a válság egyfajta "elméletét". A bemutatásból láthatóvá válik a hitelderivatívák kiemelt szerepe a válság során. A dolgozat második részében az egyik legnépszerűbb hitelderivatív termék, a szintetikus fedezett adósságkötelezettségek (CDO-k) matematikai modellezését és annak problémáit mutatjuk be. Sokak szerint ezek a matematikai modellek okozták - vagy legalábbis felerősítették - a válságot. Az elemzés során megmutatjuk, hogy nemcsak a modellezési eszközök nem voltak megfelelők, hanem az árazás elve sem állta meg a helyét a kockázatsemleges árazási keretben. Ez az eredmény élesen rámutat a mögöttes elméletek válságára. / === / The first part of the paper examines briefly the financial crisis of 2007 and its causes, focusing on its driving processes and key motifs. This shows clearly the importance and centrality of credit derivatives in the crisis. The second part presents a mathematical modelling of one of the most popular credit derivative products: synthetic collateralized debt obligations, along with the drawbacks and problems of the modelling process. It is widely claimed that these products caused or at least precipitated the crises. The authors show not only that the modelling tools were inappropriate, but that the principle for pricing did not match adequately the risk-neutral valuation framework.

Analysis of operational risk of banks – catastrophe modelling

Nowadays financial institutions due to regulation and internal motivations care more intensively on their risks. Besides previously dominating market and credit risk new trend is to handle operational risk systematically. Operational risk is the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. First we show the basic features of operational risk and its modelling and regulatory approaches, and after we will analyse operational risk in an own developed simulation model framework. Our approach is based on the analysis of latent risk process instead of manifest risk process, which widely popular in risk literature. In our model the latent risk process is a stochastic risk process, so called Ornstein- Uhlenbeck process, which is a mean reversion process. In the model framework we define catastrophe as breach of a critical barrier by the process. We analyse the distributions of catastrophe frequency, severity and first time to hit, not only for single process, but for dual process as well. Based on our first results we could not falsify the Poisson feature of frequency, and long tail feature of severity. Distribution of “first time to hit” requires more sophisticated analysis. At the end of paper we examine advantages of simulation based forecasting, and finally we concluding with the possible, further research directions to be done in the future.

Trends in research on the possible effects of climate change concerning aquatic ecosystems with special emphasis on the modelling approach

Knowledge on the expected effects of climate change on aquatic ecosystems is defined by three ways. On the one hand, long-term observation in the field serves as a basis for the possible changes; on the other hand, the experimental approach may bring valuable pieces of information to the research field. The expected effects of climate change cannot be studied by empirical approach; rather mathematical models are useful tools for this purpose. Within this study, the main findings of field observations and their implications for future were summarized; moreover, the modelling approaches were discussed in a more detailed way. Some models try to describe the variation of physical parameters in a given aquatic habitat, thus our knowledge on their biota is confined to the findings based on our present observations. Others are destined for answering special issues related to the given water body. Complex ecosystem models are the keys of our better understanding of the possible effects of climate change. Basically, these models were not created for testing the influence of global warming, rather focused on the description of a complex system (e. g. a lake) involving environmental variables, nutrients. However, such models are capable of studying climatic changes as well by taking into consideration a large set of environmental variables. Mostly, the outputs are consistent with the assumptions based on the findings in the field. Since synthetized models are rather difficult to handle and require quite large series of data, the authors proposed a more simple modelling approach, which is capable of examining the effects of global warming. This approach includes weather dependent simulation modelling of the seasonal dynamics of aquatic organisms within a simplified framework.