arXiv subjects

Pavel V. Shevchenko

Publications and source records attributed to Pavel V. Shevchenko.

63 records · Page 4Linked to original sources

arXiv2009

Dynamic operational risk: modeling dependence and combining different sources of information

In this paper, we model dependence between operational risks by allowing risk profiles to evolve stochastically in time and to be dependent. This allows for a flexible correlation structure where the dependence between frequencies of different risk categories and between severities of different risk categories as well as within risk categories can be modeled. The model is estimated using Bayesian inference methodology, allowing for combination of internal data, external data and expert opinion in the estimation procedure. We use a specialized Markov chain Monte Carlo simulation methodology known as Slice sampling to obtain samples from the resulting posterior distribution and estimate the model parameters.

q-fin.RM↗

arXiv2009

Modeling operational risk data reported above a time-varying threshold

Typically, operational risk losses are reported above a threshold. Fitting data reported above a constant threshold is a well known and studied problem. However, in practice, the losses are scaled for business and other factors before the fitting and thus the threshold is varying across the scaled data sample. A reporting level may also change when a bank changes its reporting policy. We present both the maximum likelihood and Bayesian Markov chain Monte Carlo approaches to fitting the frequency and severity loss distributions using data in the case of a time varying threshold. Estimation of the annual loss distribution accounting for parameter uncertainty is also presented.

q-fin.RM↗

arXiv2009

Implementing Loss Distribution Approach for Operational Risk

To quantify the operational risk capital charge under the current regulatory framework for banking supervision, referred to as Basel II, many banks adopt the Loss Distribution Approach. There are many modeling issues that should be resolved to use the approach in practice. In this paper we review the quantitative methods suggested in literature for implementation of the approach. In particular, the use of the Bayesian inference method that allows to take expert judgement and parameter uncertainty into account, modeling dependence and inclusion of insurance are discussed.

q-fin.RM↗

arXiv2009

Implied Correlation for Pricing multi-FX options

Option written on several foreign exchange rates (FXRs) depends on correlation between the rates. To evaluate the option, historical estimates for correlations can be used but usually they are not stable. More significantly, pricing of the option using these estimates is usually inconsistent to the traded vanilla contracts. To price options written on several FXRs with the same denominating currency, financial practitioners and traders often use implied correlations calculated from implied volatilities of FXRs that form "currency triangles". However, some options may have underlying FXRs with different denominating currencies. In this paper, we present the formula for the implied correlations between such FXRs. These can be used for valuation, for example, barrier option on two FXRs with different denominating currencies where one FXR determines how much the option is in or out of the money at maturity while another FXR is related to the barrier. Other relevant options are straightforward.

q-fin.PR↗

arXiv2009

Addressing the Impact of Data Truncation and Parameter Uncertainty on Operational Risk Estimates

Typically, operational risk losses are reported above some threshold. This paper studies the impact of ignoring data truncation on the 0.999 quantile of the annual loss distribution for operational risk for a broad range of distribution parameters and truncation levels. Loss frequency and severity are modelled by the Poisson and Lognormal distributions respectively. Two cases of ignoring data truncation are studied: the "naive model" - fitting a Lognormal distribution with support on a positive semi-infinite interval, and "shifted model" - fitting a Lognormal distribution shifted to the truncation level. For all practical cases, the "naive model" leads to underestimation (that can be severe) of the 0.999 quantile. The "shifted model" overestimates the 0.999 quantile except some cases of small underestimation for large truncation levels. Conservative estimation of capital charge is usually acceptable and the use of the "shifted model" can be justified while the "naive model" should not be allowed. However, if parameter uncertainty is taken into account (in practice it is often ignored), the "shifted model" can lead to considerable underestimation of capital charge. This is demonstrated with a practical example.

q-fin.RM↗

arXiv2009

Estimation of Operational Risk Capital Charge under Parameter Uncertainty

Many banks adopt the Loss Distribution Approach to quantify the operational risk capital charge under Basel II requirements. It is common practice to estimate the capital charge using the 0.999 quantile of the annual loss distribution, calculated using point estimators of the frequency and severity distribution parameters. The uncertainty of the parameter estimates is typically ignored. One of the unpleasant consequences for the banks accounting for parameter uncertainty is an increase in the capital requirement. This paper demonstrates how the parameter uncertainty can be taken into account using a Bayesian framework that also allows for incorporation of expert opinions and external data into the estimation procedure.

q-fin.RM↗

arXiv2009

A "Toy" Model for Operational Risk Quantification using Credibility Theory

To meet the Basel II regulatory requirements for the Advanced Measurement Approaches in operational risk, the bank's internal model should make use of the internal data, relevant external data, scenario analysis and factors reflecting the business environment and internal control systems. One of the unresolved challenges in operational risk is combining of these data sources appropriately. In this paper we focus on quantification of the low frequency high impact losses exceeding some high threshold. We suggest a full credibility theory approach to estimate frequency and severity distributions of these losses by taking into account bank internal data, expert opinions and industry data.

q-fin.RM↗

arXiv2009

Model uncertainty in claims reserving within Tweedie's compound Poisson models

In this paper we examine the claims reserving problem using Tweedie's compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the comparison of reserving quantities with and without model uncertainty incorporated into the prediction. We consider both the model selection problem and the model averaging solutions for the predicted reserves. As a part of this process we also consider the sub problem of variable selection to obtain a parsimonious representation of the model being fitted.

q-fin.RM↗

arXiv2009

The Quantification of Operational Risk using Internal Data, Relevant External Data and Expert Opinions

To quantify an operational risk capital charge under Basel II, many banks adopt a Loss Distribution Approach. Under this approach, quantification of the frequency and severity distributions of operational risk involves the bank's internal data, expert opinions and relevant external data. In this paper we suggest a new approach, based on a Bayesian inference method, that allows for a combination of these three sources of information to estimate the parameters of the risk frequency and severity distributions.

q-fin.RM↗