13,184 research outputs found
Central Limit Results for Jump-Diffusions with Mean Field Interaction and a Common Factor
A system of weakly interacting particles whose dynamics is given in terms
of jump-diffusions with a common factor is considered. The common factor is
described through another jump-diffusion and the coefficients of the evolution
equation for each particle depend, in addition to its own state value, on the
empirical measure of the states of the particles and the common factor. A
Central Limit Theorem, as , is established. The limit law is
described in terms of a certain Gaussian mixture. An application to models in
Mathematical Finance of self-excited correlated defaults is described
A default system with overspilling contagion
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
A nonparametric urn-based approach to interacting failing systems with an application to credit risk modeling
In this paper we propose a new nonparametric approach to interacting failing
systems (FS), that is systems whose probability of failure is not negligible in
a fixed time horizon, a typical example being firms and financial bonds. The
main purpose when studying a FS is to calculate the probability of default and
the distribution of the number of failures that may occur during the
observation period. A model used to study a failing system is defined default
model. In particular, we present a general recursive model constructed by the
means of inter- acting urns. After introducing the theoretical model and its
properties we show a first application to credit risk modeling, showing how to
assess the idiosyncratic probability of default of an obligor and the joint
probability of failure of a set of obligors in a portfolio of risks, that are
divided into reliability classes
Effects of Economic Interactions on Credit Risk
We study a credit risk model which captures effects of economic interactions
on a firm's default probability. Economic interactions are represented as a
functionally defined graph, and the existence of both cooperative, and
competitive, business relations is taken into account. We provide an analytic
solution of the model in a limit where the number of business relations of each
company is large, but the overall fraction of the economy with which a given
company interacts may be small. While the effects of economic interactions are
relatively weak in typical (most probable) scenarios, they are pronounced in
situations of economic stress, and thus lead to a substantial fattening of the
tails of loss distributions in large loan portfolios. This manifests itself in
a pronounced enhancement of the Value at Risk computed for interacting
economies in comparison with their non-interacting counterparts.Comment: 24 pages, 6 figure
On Pricing Basket Credit Default Swaps
In this paper we propose a simple and efficient method to compute the ordered
default time distributions in both the homogeneous case and the two-group
heterogeneous case under the interacting intensity default contagion model. We
give the analytical expressions for the ordered default time distributions with
recursive formulas for the coefficients, which makes the calculation fast and
efficient in finding rates of basket CDSs. In the homogeneous case, we explore
the ordered default time in limiting case and further include the exponential
decay and the multistate stochastic intensity process. The numerical study
indicates that, in the valuation of the swap rates and their sensitivities with
respect to underlying parameters, our proposed model outperforms the Monte
Carlo method
Default clustering in large portfolios: Typical events
We develop a dynamic point process model of correlated default timing in a
portfolio of firms, and analyze typical default profiles in the limit as the
size of the pool grows. In our model, a firm defaults at a stochastic intensity
that is influenced by an idiosyncratic risk process, a systematic risk process
common to all firms, and past defaults. We prove a law of large numbers for the
default rate in the pool, which describes the "typical" behavior of defaults.Comment: Published in at http://dx.doi.org/10.1214/12-AAP845 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Derivatives and Credit Contagion in Interconnected Networks
The importance of adequately modeling credit risk has once again been
highlighted in the recent financial crisis. Defaults tend to cluster around
times of economic stress due to poor macro-economic conditions, {\em but also}
by directly triggering each other through contagion. Although credit default
swaps have radically altered the dynamics of contagion for more than a decade,
models quantifying their impact on systemic risk are still missing. Here, we
examine contagion through credit default swaps in a stylized economic network
of corporates and financial institutions. We analyse such a system using a
stochastic setting, which allows us to exploit limit theorems to exactly solve
the contagion dynamics for the entire system. Our analysis shows that, by
creating additional contagion channels, CDS can actually lead to greater
instability of the entire network in times of economic stress. This is
particularly pronounced when CDS are used by banks to expand their loan books
(arguing that CDS would offload the additional risks from their balance
sheets). Thus, even with complete hedging through CDS, a significant loan book
expansion can lead to considerably enhanced probabilities for the occurrence of
very large losses and very high default rates in the system. Our approach adds
a new dimension to research on credit contagion, and could feed into a rational
underpinning of an improved regulatory framework for credit derivatives.Comment: 26 pages, 7 multi-part figure
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