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Papers by Younes Mouatassim
Purpose – The purpose of this paper is to introduce the zero-modified distributions in the calcul... more Purpose – The purpose of this paper is to introduce the zero-modified distributions in the calculation
of operational value-at-risk.
Design/methodology/approach – This kind of distributions is preferred when excess of zeroes is
observed. In operational risk, this phenomenon may be due to the scarcity of data, the existence of
extreme values and/or the threshold from which banks start to collect losses. In this article, the paper
focuses on the analysis of damage to physical assets.
Findings – The results show that basic Poisson distribution underestimates the dispersion, and then
leads to the underestimation of the capital charge. However, zero-modified Poisson distributions
perform well the frequency. In addition, basic negative binomial and its related zero-modified
distributions, in their turn, offer a good prediction of count events. To choose the distribution that suits
better the frequency, the paper uses the Vuong’s test. Its results indicate that zero-modified Poisson
distributions, basic negative binomial and its related zero-modified distributions are equivalent. This
conclusion is confirmed by the capital charge calculated since the differences between the six
aggregations are not significant except that of basic Poisson distribution.
Originality/value – Recently, the zero-modified formulations are widely used in many fields
because of the low frequency of the events. This article aims to describe the frequency of operational
risk using zero-modified distributions.
Keywords Operational risk, lda, Poisson distribution, Excess zeroes, Overdispersion,
Zero-inflated distributions, Hurdle distributions, Negative binomial distribution, Capital charge,
Basel II accord, Risk management, Binomial distribution
Modeling event counts is important in many fields. For this purpose, the Poisson regression model... more Modeling event counts is important in many fields. For this purpose, the Poisson regression model is often used. However, this model assumes the equidispersion of the data. Unfortunately, this assumption is often violated in the observed
data. The source of overdispersion depends on many situations. When the source of overdispersion is the excess of zeroes, the Zero-inflated Poisson regression model fits better counts data. In this paper, we first review the theoretical framework of Poisson regression and Zero-inflated Poisson regression. The probability integral transform test and the Vuong’s test are used to compare between the two models. Second, we fit these models to the number of claims in a private health insurance scheme. In our case, the number of claims is overdispersed because of the preponderance of zeroes in the data set. The results prove that Zero-inflated Poisson regression performs better the number of claims of the customers affiliated in the health insurance scheme in the Moroccan case.
Many events have contributed to the recognition of operational risk as a major problem by banks a... more Many events have contributed to the recognition of operational risk as a major problem by banks
and their regulators. Basel Committee on Banking Supervision (BCBS) adopted two innovative
features in its accord of 2004. First, it recognized operational risk as a distinct risk beside credit
and market risks. Second, the methodologies proposed to calculate capital charges for the three
types of risk become more risk-sensitive. Indeed, the advanced measurement approach aims to
permit to banks to take into account their proper exposure to risks.
In developing their proper models to quantify their exposure to operational risk, banks should take
into account the fact that there are huge differences between the behaviour of the central part and
the tail of the distribution of losses. This is especially true in the case of losses characterized by the
so-called low frequency-high severity losses.
In this paper, mixture models with a probability concentration for the zeros losses are fitted to our
dataset. We used separately a lognormal distribution and a gamma distribution in the mixture
models. Such models capture differently tail behaviour and allow to take into account the features
that are important for operational risk modelling; that is: the existence of zeros, positive skewness
and heavy tailedness of data. Both fits are done with a data on the damages of physical assets
incurred by a Moroccan bank during two years. Results show significant differences when the
lognormal or the gamma mixture models are used to evaluate capital at risk or equivalently return
period of a given loss and confirm the discussion on distributions tails related to the importance of
model selection.
Purpose – The purpose of this paper is to introduce the zero-modified distributions in the calcul... more Purpose – The purpose of this paper is to introduce the zero-modified distributions in the calculation
of operational value-at-risk.
Design/methodology/approach – This kind of distributions is preferred when excess of zeroes is
observed. In operational risk, this phenomenon may be due to the scarcity of data, the existence of
extreme values and/or the threshold from which banks start to collect losses. In this article, the paper
focuses on the analysis of damage to physical assets.
Findings – The results show that basic Poisson distribution underestimates the dispersion, and then
leads to the underestimation of the capital charge. However, zero-modified Poisson distributions
perform well the frequency. In addition, basic negative binomial and its related zero-modified
distributions, in their turn, offer a good prediction of count events. To choose the distribution that suits
better the frequency, the paper uses the Vuong’s test. Its results indicate that zero-modified Poisson
distributions, basic negative binomial and its related zero-modified distributions are equivalent. This
conclusion is confirmed by the capital charge calculated since the differences between the six
aggregations are not significant except that of basic Poisson distribution.
Originality/value – Recently, the zero-modified formulations are widely used in many fields
because of the low frequency of the events. This article aims to describe the frequency of operational
risk using zero-modified distributions.
Keywords Operational risk, lda, Poisson distribution, Excess zeroes, Overdispersion,
Zero-inflated distributions, Hurdle distributions, Negative binomial distribution, Capital charge,
Basel II accord, Risk management, Binomial distribution
Modeling event counts is important in many fields. For this purpose, the Poisson regression model... more Modeling event counts is important in many fields. For this purpose, the Poisson regression model is often used. However, this model assumes the equidispersion of the data. Unfortunately, this assumption is often violated in the observed
data. The source of overdispersion depends on many situations. When the source of overdispersion is the excess of zeroes, the Zero-inflated Poisson regression model fits better counts data. In this paper, we first review the theoretical framework of Poisson regression and Zero-inflated Poisson regression. The probability integral transform test and the Vuong’s test are used to compare between the two models. Second, we fit these models to the number of claims in a private health insurance scheme. In our case, the number of claims is overdispersed because of the preponderance of zeroes in the data set. The results prove that Zero-inflated Poisson regression performs better the number of claims of the customers affiliated in the health insurance scheme in the Moroccan case.
Many events have contributed to the recognition of operational risk as a major problem by banks a... more Many events have contributed to the recognition of operational risk as a major problem by banks
and their regulators. Basel Committee on Banking Supervision (BCBS) adopted two innovative
features in its accord of 2004. First, it recognized operational risk as a distinct risk beside credit
and market risks. Second, the methodologies proposed to calculate capital charges for the three
types of risk become more risk-sensitive. Indeed, the advanced measurement approach aims to
permit to banks to take into account their proper exposure to risks.
In developing their proper models to quantify their exposure to operational risk, banks should take
into account the fact that there are huge differences between the behaviour of the central part and
the tail of the distribution of losses. This is especially true in the case of losses characterized by the
so-called low frequency-high severity losses.
In this paper, mixture models with a probability concentration for the zeros losses are fitted to our
dataset. We used separately a lognormal distribution and a gamma distribution in the mixture
models. Such models capture differently tail behaviour and allow to take into account the features
that are important for operational risk modelling; that is: the existence of zeros, positive skewness
and heavy tailedness of data. Both fits are done with a data on the damages of physical assets
incurred by a Moroccan bank during two years. Results show significant differences when the
lognormal or the gamma mixture models are used to evaluate capital at risk or equivalently return
period of a given loss and confirm the discussion on distributions tails related to the importance of
model selection.