Issue |
ESAIM: ProcS
Volume 56, 2017
Enlargement of filtrations
|
|
---|---|---|
Page(s) | 1 - 21 | |
DOI | https://doi.org/10.1051/proc/201756001 | |
Published online | 04 September 2017 |
From the decompositions of a stopping time to risk premium decompositions*
Department of Banking and Finance University of Zürich, Plattenstrasse 32 Zürich 8032, Switzerland
The occurrence of some events can impact asset prices and produce losses. The amplitude of these losses are partly determined by the degree of predictability of those events by the market investors, as risk premiums build up in an asset price as a compensation of the anticipated losses. The aim of this paper is to propose a general framework where these phenomena can be properly defined and quantified.
Our focus are the default events and the defaultable assets, but the framework could apply to any event whose occurrence impacts some asset prices.
We provide the general construction of a default time under the so called (H) hypothesis, which reveals a useful way in which default models can be built, using both market factors and idiosyncratic factors. All the relevant characteristics of a default time (i.e. the Azéma supermartingale and its Doob-Meyer decomposition) are explicitly computed given the information about these factors.
We then define the default event risk premiums and the default adjusted probability measure. These concepts are useful for pricing defaultable claims in a framework that includes possible economic shocks, such as jumps of the recovery process or of some default-free assets at the default time. These formulas are not classic and we point out that the knowledge of the default compensator (or the intensity process when the default time is totally inaccessible) is not a sufficient quantity for finding explicit prices; the Azéma supermartingale and its Doob-Meyer decomposition are needed. The progressive enlargement of a filtration framework is the right tool for pricing defaultable claims in non standard frameworks where non defaultable assets or recovery processes may react at the default event.
© EDP Sciences, SMAI 2017
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.