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

Medvegyev, Péter and Plank, Péter (2011) Intenzitásalapú modellezés és a mértékcsere (Intensity-based modeling and thje change of measure). Szigma, 42 (3-4). pp. 79-104.

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Abstract

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.

Item Type:Article
Subjects:Mathematics, Econometrics
ID Code:1285
Deposited By: Ádám Hoffmann
Deposited On:03 Jul 2013 10:30
Last Modified:03 Jul 2013 10:30

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