Operational Risk Modeling Analytics phần 1 ppsx

[...]... exceedences 7.8 .1 From a fixed number of losses 7.8.2 From a random number of losses 7.9 Stability of excesses of the generalized Pareto 7 .10 Mean excess function 7 .11 Limiting distributions of excesses 7 .12 T V a R for extreme value distributions 7 .13 Further reading 7 .14 Exercises 17 4 17 5 17 8 17 9 17 9 18 0 18 3 18 7 18 7 19 0 19 1 19 1 19 2 19 4 19 8 19 8 205 205 207 208 208 21 0 213 214 21 7 21 9 2 21 2 21 222 226... 10 .6 Exercises 283 283 286 289 289 2 91 293 293 297 304 304 307 315 31 6 x CONTENTS 11 Estimation for discrete distributions 11 .1 Introduction 11 .2 Poisson distribution 11 .3 Negative binomial distribution 11 .4 Binomial distribution 11 .5 The (a, 1) class b, 11 .6 Compound models 11 .7 EYgPect of exposure o n maximum likelihood estimation 11 .8 Exercises 329 329 329 12 Model selection 12 .1 Introduction 12 .2... 75 277 280 10 Parameter estimation 10 .1 Introduction 10 .2 Method of moments and percentile matching 10 .3 M a x i m u m likelihood estimation 10 .3 .1 Introduction 10 .3.2 Complete, individual data 10 .3.3 Complete, grouped data 10 .3.4 Truncated or censored data 10 .4 Variance and interval estimation 10 .5 Bayesian estimation 10 .5 .1 Definitions and Bayes ’ theorem 10 .5.2 Inference and prediction 10 .5.3 Computational... of regulatory capital, risk- weighted assets, and the minimum ratio of capital to risk- weighted assets Risks are categorized into five categories: INTRODUCTION 7 1 credit risk 2 market risk 3 operational risk 4 liquidity risk 5 legal risk Explicit and separate minimum capital requirements for operational risk have been added to the Base1 I1 framework Specifically for operational risk, there is a range... model 12 .3 Graphical comparison of the density and distribution functions 12 .4 Hypothesis tests 22.4 .1 Kolmogorov-Smirnov test 12 .4.2 Anderson-Darling test 12 .4.3 Chi-square goodness-of-fit test 12 .44 Likelihood ratio test 12 .5 Selecting a model 12 .5 .1 Introduction 12 .5.2 Judgment-based approaches 12 .5.3 Score- based approaches 12 .6 Exercises 34 9 34 9 350 13 Fitting extreme value models 13 .1 Introduction... the model THE MODEL-BASED APPROACH c 15 t I Fig 1. 1 The modeling process 1. 4 .1 The modeling process The modeling process is illustrated in Figure 1. 1,which describes six stages Stage 1 One or more models are selected based on the risk analyst’s prior knowledge and experience and possibly on the nature and form of available data In studies of the size of operational risk losses, a set of statistical distributions,... from operational risk events This better understanding of operational risk should have a direct effect on the operational risk by identifying areas where the bank can reduce both the frequency and the severity of those events Pillar 11 1: Market discipline The objective of Pillar I 11 is to encourage market discipline by developing a set of disclosure requirements that will allow 8 OPERATIONAL RISK market... Introduction 13 .2 Parameter estimation 13 .2 .1 M L estimation f r o m the extreme value distribution 13 .2.2 M L estimation from the generalized Pareto distribution 13 .2.3 Estimating the Pareto shape parameter 13 .2.4 Estimating extreme probabilities 13 .3 Model selection 13 .3 .1 Mean excess plots 383 383 384 333 336 338 34 3 344 34 5 3 51 356 357 360 360 365 367 367 368 368 375 384 387 389 3 91 392 392 CONTENTS XI 14 ... are therefore subject to risks of different sizes Although operational risk was originally defined t o capture all sources of risk other than market and credit risk, several more specific definitions of operational risk have become well-known In a paper published in 19 98, the Basel Committee 1 1 on Banking Supervision (BCBS) identified the most important 9 aspects of operational risk as relating to breakdowns... include legal risks but exclude strategic, reputational risk and systemic risks There remains some controversy over these items Is a strategic decision that is later found to be in error really an operational risk? Is a loss in reputation an operational risk or simply the result of an operational risk event? Operational risk in the banking sector is believed to represent about 30% of the total risk assumed . of excesses 7 .12 TVaR for extreme value distributions 7 .13 Further reading 7 .14 Exercises 17 4 17 5 17 8 17 9 17 9 18 0 18 3 18 7 18 7 19 0 19 1 19 1 19 2 1 94 19 8 19 8 205 205 207. Operational risk 1. 1 Introduction 1. 1 .1 Basel 11 - General 1. 1.2 1. 2 Operational risk in insurance 1. 3 The analysis of operational risk 1. 4 The model-based approach 1. 4 .1 The modeling. distributions 11 .1 Introduction 11 .2 Poisson distribution 11 .3 Negative binomial distribution 1 1. 4 Binomial distribution 11 .5 The (a, b, 1) class 11 .6 Compound models 11 .7 EYgPect