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From the decompositions of a stopping times to risk premium decompositions


Coculescu, Delia (2017). From the decompositions of a stopping times to risk premium decompositions. ESAIM: Proceedings and Surveys, 60:1-60.

Abstract

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 Azema 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 Azema 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.

Abstract

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 Azema 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 Azema 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:June 2017
Deposited On:23 May 2017 13:52
Last Modified:24 May 2017 03:09
Publisher:EDP Sciences
ISSN:2267-3059
Other Identification Number:merlin-id:14840

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