3,971 research outputs found
Optimal investment under multiple defaults risk: A BSDE-decomposition approach
We study an optimal investment problem under contagion risk in a financial
model subject to multiple jumps and defaults. The global market information is
formulated as a progressive enlargement of a default-free Brownian filtration,
and the dependence of default times is modeled by a conditional density
hypothesis. In this Ito-jump process model, we give a decomposition of the
corresponding stochastic control problem into stochastic control problems in
the default-free filtration, which are determined in a backward induction. The
dynamic programming method leads to a backward recursive system of quadratic
backward stochastic differential equations (BSDEs) in Brownian filtration, and
our main result proves, under fairly general conditions, the existence and
uniqueness of a solution to this system, which characterizes explicitly the
value function and optimal strategies to the optimal investment problem. We
illustrate our solutions approach with some numerical tests emphasizing the
impact of default intensities, loss or gain at defaults and correlation between
assets. Beyond the financial problem, our decomposition approach provides a new
perspective for solving quadratic BSDEs with a finite number of jumps.Comment: Published in at http://dx.doi.org/10.1214/11-AAP829 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Dynamics of multivariate default system in random environment
We consider a multivariate default system where random environmental
information is available. We study the dynamics of the system in a general
setting and adopt the point of view of change of probability measures. We also
make a link with the density approach in the credit risk modelling. In the
particular case where no environmental information is concerned, we pay a
special attention to the phenomenon of system weakened by failures as in the
classical reliability system
Common Failings: How Corporate Defaults are Correlated
We develop, and apply to data on U.S. corporations from 1979-2004, tests of the standard doubly-stochastic assumption under which firms'default times are correlated only as implied by the correlation of factors determining their default intensities. This assumption is violated in the presence of contagion or "frailty" (unobservable explanatory variables that are correlated across firms). Our tests do not depend on the time-series properties of default intensities. The data do not support the joint hypothesis of well specified default intensities and the doubly-stochastic assumption. There is also some evidence of default clustering in excess of that implied by the doubly-stochastic model with the given intensities.
Stochastic control under progressive enlargement of filtrations and applications to multiple defaults risk management
We formulate and investigate a general stochastic control problem under a
progressive enlargement of filtration. The global information is enlarged from
a reference filtration and the knowledge of multiple random times together with
associated marks when they occur. By working under a density hypothesis on the
conditional joint distribution of the random times and marks, we prove a
decomposition of the original stochastic control problem under the global
filtration into classical stochastic control problems under the reference
filtration, which are determined in a finite backward induction. Our method
revisits and extends in particular stochastic control of diffusion processes
with finite number of jumps. This study is motivated by optimization problems
arising in default risk management, and we provide applications of our
decomposition result for the indifference pricing of defaultable claims, and
the optimal investment under bilateral counterparty risk. The solutions are
expressed in terms of BSDEs involving only Brownian filtration, and remarkably
without jump terms coming from the default times and marks in the global
filtration
Levy subordinator model: A two parameter model of default dependency
The May 2005 crisis and the recent credit crisis have indicated to us that any realistic model of default dependency needs to account for at least two risk factors, firm-specific and catastrophic. Unfortunately, the popular Gaussian copula model has no identifiable support to either of these. In this article, a two parameter model of default dependency based on the Levy subordinator is presented accounting for these two risk factors. Subordinators are Levy processes with non-decreasing sample paths. They help ensure that the loss process is non-decreasing leading to a promising class of dynamic models. The simplest subordinator is the Levy subordinator, a maximally skewed stable process with index of stability 1/2. Interestingly, this simplest subordinator turns out to be the appropriate choice as the basic process in modeling default dependency. Its attractive feature is that it admits a closed form expression for its distribution function. This helps in automatic calibration to individual hazard rate curves and efficient pricing with Fast Fourier Transform techniques. It is structured similar to the one-factor Gaussian copula model and can easily be implemented within the framework of the existing infrastructure. As it turns out, the Gaussian copula model can itself be recast into this framework highlighting its limitations. The model can also be investigated numerically with a Monte Carlo simulation algorithm. It admits a tractable framework of random recovery. It is investigated numerically and the implied base correlations are presented over a wide range of its parameters. The investigation also demonstrates its ability to generate reasonable hedge ratios
Scope for Credit Risk Diversification
This paper considers a simple model of credit risk and derives the limit distribution of losses under different assumptions regarding the structure of systematic risk and the nature of exposure or firm heterogeneity. We derive fat-tailed correlated loss distributions arising from Gaussian risk factors and explore the potential for risk diversification. Where possible the results are generalised to non-Gaussian distributions. The theoretical results indicate that if the firm parameters are heterogeneous but come from a common distribution, for sufficiently large portfolios there is no scope for further risk reduction through active portfolio management. However, if the firm parameters come from different distributions, then further risk reduction is possible by changing the portfolio weights. In either case, neglecting parameter heterogeneity can lead to underestimation of expected losses. But, once expected losses are controlled for, neglecting parameter heterogeneity can lead to overestimation of risk, whether measured by unexpected loss or value-at-risk
On the Determinants of the Implied Default Barrier
We use the maximum likelihood (ML) estimation approach to estimate the default barriers from market values of equities for a sample of 762 public industrial Canadian firms. The ML approach allows us to estimate the asset instantaneous drift, volatility and barrier level simultaneously, when the firm's equity is priced as a Down-and-Out European call (DOC) option. We find that the estimated barrier is positive and significant in our sample. Moreover, we compare the default prediction accuracy of the DOC framework with the KMV-Merton approach. Using probit estimation, we find that the default probability from the two structural models provides similar in-sample fits, but the barrier option framework achieves better out-of-sample forecasts. Regression analysis shows that leverage is not the only determinant of the default barrier. The implied default threshold is also positively related to financing costs, and negatively to liquidity, asset volatility and firm size. We also find that liquidation costs, renegotiation frictions and equity holders' bargaining power increase the implied default barrier level.Barrier option, default barrier, bankruptcy prediction, maximum likelihood estimation, strategic default
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