Moody's correlated binomial default distributions for inhomogeneous portfolios

Mori, Shintaro; Kitsukawa, K.; Hisakado, Masato

doi:10.1080/14697680903419685

Cited by 6 publications

(4 citation statements)

References 22 publications

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“…Credit default swap is one of tools to hedge credit risks. These products protect against a subset of the total loss on a credit portfolio in exchange for payments and provide valuable insights into market implications on default dependencies, such as the clustering of defaults [1][2][3][4]. This aspect is important because the difficulties in managing credit events depend on correlations.…”

Section: Introductionmentioning

confidence: 99%

Multi-Dimensional self-exciting NBD process and Default portfolios

Hisakado¹,

Hattori²,

Mori³

2022

Preprint

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In this article we apply the multi dimensional self exciting negative binomial distribution (SE-NBD) process to the default portfolios which have 13 sectors. SE-NBD process is the Poisson process with the gamma distributed intensity function. We extend SE-NBD process to the multi dimensional process. Using the multi dimensional SE-NBD process (MD-SE-NBD), we can estimate the interactions of among these sectors as the network. Applying the impact analysis, we can classify the upstream and downstream sectors. The upstream sectors are the real estate and financial institution (FI) sectors. From these upstream sectors the shock spreads to the downstream sectors and returns to the upstream sectors. This is the amplifier of the shock. It is consistent with the narrative understandings of the bubble burst. We compare these results to the multi dimensional Hawkes process (MD-Hawkes) which has the zero variance intensity function.

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Section: Introductionmentioning

confidence: 99%

Multi-Dimensional self-exciting NBD process and Default portfolios

Hisakado¹,

Hattori²,

Mori³

2022

Preprint

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“…These products protect against a subset of the total loss on a credit portfolio in exchange for payments, and provide valuable insights into the market implications of default dependencies and clustering of defaults [20][21][22]. This aspect is important, because the difficulties in managing credit events depend on these correlations.…”

Section: Introductionmentioning

confidence: 99%

From the multi-terms urn model to the self-exciting negative binomial distribution and Hawkes processes

Hisakado,

Hattori,

Mori

2021

Preprint

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This study considers a new multi-term urn process that has a correlation in the same term and temporal correlation. The objective is to clarify the relationship between the urn model and the Hawkes process. Correlation in the same term is represented by the Pólya urn model and the temporal correlation is incorporated by introducing the conditional initial condition. In the double-scaling limit of this urn process, the self-exciting negative binomial distribution (SE-NBD) process, which is a marked point process, is obtained. In the standard continuous limit, this process becomes the Hawkes process, which has no correlation in the same term. The difference is the variance of the intensity function in that the phase transition from the steady to the non-steady state can be observed. The critical point, at which the power law distribution is obtained, is the same for the Hawkes and the urn processes. These two processes are used to analyze empirical data of financial default to estimate the parameters of the model. For the default portfolio, the results produced by the urn process are superior to those obtained with the Hawkes process and confirm self-excitation.

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“…Estimations of the probability of default (PD) and default correlation have been obtained from empirical studies on the historical data from credit events. These two parameters are important for pricing financial products such as synthetic CDOs [15][16][17]. Also called "long run PDs", these parameters are important to financial institutions for portfolio management.…”

Section: Introductionmentioning

confidence: 99%

Phase transition in the Bayesian estimation of the default portfolio

Hisakado

Mori

2020

Physica A: Statistical Mechanics and its Applications

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The probability of default (PD) estimation is an important process for financial institutions.The difficulty of the estimation depends on the correlations between borrowers. In this paper, we introduce a hierarchical Bayesian estimation method using the beta binomial distribution and consider a multi-year case with a temporal correlation. A phase transition occurs when the temporal correlation decays by power decay. When the power index is less than one, the PD estimator does not converge. It is difficult to estimate the PD with limited historical data. Conversely, when the power index is greater than one, the convergence is the same as that of the binomial distribution.We provide a condition for the estimation of the PD and discuss the universality class of the phase transition. We investigate the empirical default data history of rating agencies and their Fourier transformations to confirm the the form of the correlation decay. The power spectrum of the decay history seems to be 1/f, which corresponds to a long memory. But the estimated power index is much greater than one. If we collect adequate historical data, the parameters can be estimated correctly.

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Moody's correlated binomial default distributions for inhomogeneous portfolios

Cited by 6 publications

References 22 publications

Multi-Dimensional self-exciting NBD process and Default portfolios

Multi-Dimensional self-exciting NBD process and Default portfolios

From the multi-terms urn model to the self-exciting negative binomial distribution and Hawkes processes

Phase transition in the Bayesian estimation of the default portfolio

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