Dynamics of multivariate default system in random environment

Jeanblanc, Monique; Jiao, Ying

doi:10.1016/j.spa.2017.03.017

Cited by 5 publications

(8 citation statements)

References 35 publications

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“…However the goals of [11,12] are very different compared to the current paper as the authors do not consider hypothesis (H ) and do not compute the semimartingale decomposition in the enlarged filtration. In [11], for pricing purposes, the authors have focused their computational efforts on the F τ 1:kconditional expectation, the F τ 1:k -intensity of default and the characterization of F τ 1:k -martingales in the case ordered default times and have only commented on the link between the density of non-ordered default times and ordered default times (see section 5.1 within [11] or (5.7) below).…”

Section: Computation Under the Density Hypothesismentioning

confidence: 91%

“…In the recent works of El-Karoui et al [11,12], the authors have also considered multiple default times under the density hypothesis (Jacod's criteria). However the goals of [11,12] are very different compared to the current paper as the authors do not consider hypothesis (H ) and do not compute the semimartingale decomposition in the enlarged filtration.…”

Section: Computation Under the Density Hypothesismentioning

confidence: 99%

“…In [11], for pricing purposes, the authors have focused their computational efforts on the F τ 1:kconditional expectation, the F τ 1:k -intensity of default and the characterization of F τ 1:k -martingales in the case ordered default times and have only commented on the link between the density of non-ordered default times and ordered default times (see section 5.1 within [11] or (5.7) below). While in [12], the authors studied similar problems to that of [11] and the form of the F τ 1:k and F τ -conditional expectations for non-ordered default times was stated without computation in (26) within and much of the computational effort was devoted to the characterization of F τ 1:k -martingales.…”

Section: Computation Under the Density Hypothesismentioning

confidence: 99%

“…The study of reduced form credit risk models with multiple defaults have recently been considered in [7,11,12] and [24] through the framework of progressive enlargement of a base filtration F with multiple random times. In [7] and [24], under Jacod's absolute continuity criteria, the authors focused on optimization and mean variance hedging problems in the progressive enlargement of F with non-ordered random times.…”

Section: Introductionmentioning

confidence: 99%

“…By rewriting the non-ordered random times into ordered random times with random marks, the authors of [7] and [24] have effectively reduced the problem to the case of multiple ordered random times. On the other hand, the authors of [11] and [12] have focused on the pricing problem by computing, again under the Jacod's criteria, the conditional expectation and the stochastic intensity of the default times in the progressive enlargement of F with ordered and non-ordered random times. In this work, we focus on the computation of the semimartingale decomposition of F-martingales in some enlargement of F, for which the progressive enlargement with multiple non-ordered random times is a special case.…”

Section: Introductionmentioning

confidence: 99%

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An enlargement of filtration formula with applications to multiple non-ordered default times

Jeanblanc

Song

2017

Finance Stoch

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In this work, for a reference filtration F, we develop a method for computing the semimartingale decomposition of F-martingales in a specific type of enlargement of F. As an application, we study the progressive enlargement of F with a sequence of non-ordered default times and we show how to deduce results concerning the first-to-default, k-th-to-default, k-out-ofn-to-default or the all-to-default events. In particular, using this method, we compute explicitly the semimartingale decomposition of F-martingales under the absolute continuity condition of Jacod.

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Section: Computation Under the Density Hypothesismentioning

confidence: 91%

Section: Computation Under the Density Hypothesismentioning

confidence: 99%

Section: Computation Under the Density Hypothesismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An enlargement of filtration formula with applications to multiple non-ordered default times

Jeanblanc

Song

2017

Finance Stoch

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Computing the probability of a financial market failure: a new measure of systemic risk

2022

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A Default System with Overspilling Contagion

Coculescu

2017

SSRN Journal

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Abstract. In classical contagion models, default systems are Markovian conditionally on the observation of their stochastic environment, with interacting intensities. This necessitates that the environment evolves autonomously and is not influenced by the history of the default events. We extend the classical literature and allow a default system to have a contagious impact on its environment. In our framework, contagion can either be contained within the default system (i.e., direct contagion from a counterparty to another) or spill from the default system over its environment (indirect contagion). This type of model is of interest whenever one wants to capture within a model possible impacts of the defaults of a class of debtors on the more global economy and vice versa. Motivation and aimsDefault events tend to cluster in time, a phenomenon that arises from diverse causes. The literature on dynamic modelling of defaults proposed so far two major mechanisms that produce this effect. First, there is the so-called cyclical correlation, i.e., the dependence of the debtors' financial situation on some common factors. One can naturally think of some macroeconomic factors that impact the default probabilities of many debtors at a time, as the interest rates, the prices of some commodities or the business cycle; a purely statistical approach using abstract or unobserved factors is also possible. Secondly, there is the socalled counterparty risk or direct contagion, i.e., the default of one debtor represents itself a destabilising factor impacting the default rates of surviving debtors (the counterparties of a defaulted debtor). In order to have these two mechanisms of contagion operational simultaneously it is necessary to distinguish within the model the default system from its environment. The role of the random environment is to carry the cyclical dependence.The most classical approach so far was to consider that conditionally on a given realisation of the random environment, the vector of default indicator processes of the different debtors is a time inhomogeneous Markov chain.While the Markovian assumption is convenient, it necessitates that the environment evolves autonomously and is not influenced by the history of the default events. Our aim here is precisely to remove this assumption. This equates to introducing a new source of contagion, that we call overspilling (or indirect) contagion: the one that transmits from the default system to its environment, subsequently having a feedback effect on the system itself. The construction, by its nature is not Markovian, the default probabilities depend not only on the current state of the default system, but also on the circumstances of the occurrence of the past defaults, more precisely the knowledge of their impact on the environment. The theory of enlargements of filtrations reveals to be the right tool to deal with this non Markovian framework.

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Dynamics of multivariate default system in random environment

Cited by 5 publications

References 35 publications

An enlargement of filtration formula with applications to multiple non-ordered default times

An enlargement of filtration formula with applications to multiple non-ordered default times

Computing the probability of a financial market failure: a new measure of systemic risk

A Default System with Overspilling Contagion

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