
Modelling Operational Risk Using Bayesian Inference
Hardcover | 21 January 2011
At a Glance
322 Pages
22.86 x 15.88 x 2.54
Hardcover
$169.00
or 4 interest-free payments of $42.25 with
orShips in 5 to 7 business days
The management of operational risk in the banking industry has undergone explosive changes over the last decade due to substantial changes in the operational environment. Globalization, deregulation, the use of complex financial products, and changes in information technology have resulted in exposure to new risks which are very different from market and credit risks. In response, the Basel Committee on Banking Supervision has developed a new regulatory framework for capital measurement and standards for the banking sector. This has formally defined operational risk and introduced corresponding capital requirements.
Many banks are undertaking quantitative modelling of operational risk using the Loss Distribution Approach (LDA) based on statistical quantification of the frequency and severity of operational risk losses. There are a number of unresolved methodological challenges in the LDA implementation. Overall, the area of quantitative operational risk is very new and different methods are under hot debate.
This book is devoted to quantitative issues in LDA. In particular, the use of Bayesian inference is the main focus. Though it is very new in this area, the Bayesian approach is well suited for modelling operational risk, as it allows for a consistent and convenient statistical framework for quantifying the uncertainties involved. It also allows for the combination of expert opinion with historical internal and external data in estimation procedures. These are critical, especially for low-frequency/high-impact operational risks.
This book is aimed at practitioners in risk management, academic researchers in financial mathematics, banking industry regulators and advanced graduate students in the area. It is a must-read for anyone who works, teaches or does research in the area of financial risk.
Industry Reviews
From the reviews:
"This hands-on book provides a very good overview of the loss distribution approach (LDA). ... The book is written in a mathematical format which allows practitioners, (advanced) graduate students (who may well be social science students) and researchers to access the concepts in a fairly straightforward way. ... unique feature of the book is the use of abstracts which precede the start of each of the main chapters. ... book also contains a useful appendix with a list of the functional forms of key distributions." (Emmanuel Haven, Mathematical Reviews, Issue 2012 d)| Operational Risk and Basel II | p. 1 |
| Introduction to Operational Risk | p. 1 |
| Defining Operational Risk | p. 4 |
| Basel II Approaches to Quantify Operational Risk | p. 4 |
| Loss Data Collections | p. 7 |
| 2001 LDCE | p. 10 |
| 2002 LDCE | p. 11 |
| 2004 LDCE | p. 13 |
| 2007 LDCE | p. 15 |
| General Remarks | p. 16 |
| Operational Risk Models | p. 17 |
| Loss Distribution Approach | p. 21 |
| Loss Distribution Model | p. 21 |
| Operational Risk Data | p. 22 |
| A Note on Data Sufficiency | p. 24 |
| Insurance | p. 25 |
| Basic Statistical Concepts | p. 26 |
| Random Variables and Distribution Functions | p. 26 |
| Quantiles and Moments | p. 29 |
| Risk Measures | p. 32 |
| Capital Allocation | p. 33 |
| Euler Allocation | p. 34 |
| Allocation by Marginal Contributions | p. 36 |
| Model Fitting: Frequentist Approach | p. 37 |
| Maximum Likelihood Method | p. 39 |
| Bootstrap | p. 42 |
| Bayesian Inference Approach | p. 43 |
| Conjugate Prior Distributions | p. 45 |
| Gaussian Approximation for Posterior | p. 46 |
| Posterior Point Estimators | p. 46 |
| Restricted Parameters | p. 47 |
| Noninformative Prior | p. 48 |
| Mean Square Error of Prediction | p. 49 |
| Markov Chain Monte Carlo Methods | p. 50 |
| Metropolis-Hastings Algorithm | p. 52 |
| Gibbs Sampler | p. 53 |
| Random Walk Metropolis-Hastings Within Gibbs | p. 54 |
| ABC Methods | p. 56 |
| Slice Sampling | p. 58 |
| MCMC Implementation Issues | p. 60 |
| Tuning, Burn-in and Sampling Stages | p. 60 |
| Numerical Error | p. 62 |
| MCMC Extensions | p. 65 |
| Bayesian Model Selection | p. 66 |
| Reciprocal Importance Sampling Estimator | p. 68 |
| Deviance Information Criterion | p. 68 |
| Problems | p. 69 |
| Calculation of Compound Distribution | p. 71 |
| Introduction | p. 71 |
| Analytic Solution via Convolutions | p. 72 |
| Analytic Solution via Characteristic Functions | p. 73 |
| Compound Distribution Moments | p. 76 |
| Value-at-Risk and Expected Shortfall | p. 78 |
| Monte Carlo Method | p. 79 |
| Quantile Estimate | p. 80 |
| Expected Shortfall Estimate | p. 82 |
| Panjer Recursion | p. 83 |
| Discretisation | p. 85 |
| Computational Issues | p. 87 |
| Panjer Extensions | p. 88 |
| Panjer Recursion for Continuous Severity | p. 89 |
| Fast Fourier Transform | p. 89 |
| Compound Distribution via FFT | p. 91 |
| Aliasing Error and Tilting | p. 92 |
| Direct Numerical Integration | p. 94 |
| Forward and Inverse Integrations | p. 94 |
| Gaussian Quadrature for Subdivisions | p. 98 |
| Tail Integration | p. 100 |
| Comparison of Numerical Methods | p. 103 |
| Closed-Form Approximation | p. 105 |
| Normal and Translated Gamma Approximations | p. 105 |
| VaR Closed-Form Approximation | p. 106 |
| Problems | p. 108 |
| Bayesian Approach for LDA | p. 111 |
| Introduction | p. 111 |
| Combining Different Data Sources | p. 114 |
| Ad-hoc Combining | p. 114 |
| Example of Scenario Analysis | p. 116 |
| Bayesian Method to Combine Two Data Sources | p. 117 |
| Estimating Prior: Pure Bayesian Approach | p. 119 |
| Estimating Prior: Empirical Bayesian Approach | p. 121 |
| Poisson Frequency | p. 121 |
| The Lognormal LN(¿, ¿) Severity with Unknown ¿ | p. 126 |
| The Lognormal LN(¿, ¿) Severity with Unknown ¿ and ¿ | p. 129 |
| Pareto Severity | p. 131 |
| Estimation of the Prior Using Data | p. 136 |
| The Maximum Likelihood Estimator | p. 136 |
| Poisson Frequencies | p. 137 |
| Combining Expert Opinions with External and Internal Data | p. 140 |
| Conjugate Prior Extension | p. 142 |
| Modelling Frequency: Poisson Model | p. 143 |
| Modelling Frequency: Poission with Stochastic Intensity | p. 150 |
| Lognormal Model for Severities | p. 153 |
| Pareto Model | p. 156 |
| Combining Data Sources Using Credibility Theory | p. 159 |
| Bühlmann-Straub Model | p. 161 |
| Modelling Frequency | p. 163 |
| Modelling Severity | p. 166 |
| Numerical Example | p. 169 |
| Remarks and Interpretation | p. 170 |
| Capital Charge Under Parameter Uncertainty | p. 171 |
| Predictive Distributions | p. 171 |
| Calculation of Predictive Distributions | p. 173 |
| General Remarks | p. 175 |
| Problems | p. 177 |
| Addressing the Data Truncation Problem | p. 179 |
| Introduction | p. 179 |
| Constant Threshold-Poisson Process | p. 181 |
| Maximum Likelihood Estimation | p. 182 |
| Bayesian Estimation | p. 186 |
| Extension to Negative Binomial and Binomial Frequencies | p. 188 |
| Ignoring Data Truncation | p. 192 |
| Threshold Varying in Time | p. 196 |
| Problems | p. 200 |
| Modelling Large Losses | p. 203 |
| Introduction | p. 203 |
| EVT - Block Maxima | p. 204 |
| EVT - Threshold Exceedances | p. 208 |
| A Note on GPD Maximum Likelihood Estimation | p. 212 |
| EVT - Random Number of Losses | p. 214 |
| EVT - Bayesian Approach | p. 216 |
| Subexponential Severity | p. 221 |
| Flexible Severity Distributions | p. 225 |
| g-and-h Distribution | p. 225 |
| GB2 Distribution | p. 227 |
| Lognormal-Gamma Distribution | p. 228 |
| Generalised Champernowne Distribution | p. 229 |
| ¿-Stable Distribution | p. 230 |
| Problems | p. 232 |
| Modelling Dependence | p. 235 |
| Introduction | p. 235 |
| Dominance of the Heaviest Tail Risks | p. 238 |
| A Note on Negative Diversification | p. 240 |
| Copula Models | p. 241 |
| Gaussian Copula | p. 242 |
| Archimedean Copulas | p. 243 |
| t-Copula | p. 245 |
| Dependence Measures | p. 247 |
| Linear Correlation | p. 247 |
| Spearman's Rank Correlation | p. 248 |
| Kendall's tau Rank Correlation | p. 249 |
| Tail Dependence | p. 250 |
| Dependence Between Frequencies via Copula | p. 251 |
| Common Shock Processes | p. 252 |
| Dependence Between Aggregated Losses via Copula | p. 253 |
| Dependence Between the k-th Event Times/Losses | p. 253 |
| Modelling Dependence via Lévy Copulas | p. 253 |
| Structural Model with Common Factors | p. 254 |
| Stochastic and Dependent Risk Profiles | p. 256 |
| Dependence and Combining Different Data Sources | p. 260 |
| Bayesian Inference Using MCMC | p. 262 |
| Numerical Example | p. 264 |
| Predictive Distribution | p. 266 |
| Problems | p. 269 |
| List of Distributions | p. 273 |
| Discrete Distributions | p. 273 |
| Poisson Distribution, Poisson(¿) | p. 273 |
| Binomial Distribution, Bin(n, p) | p. 274 |
| Negative Binomial Distribution, Neg Bin(r, p) | p. 274 |
| Continuous Distributions | p. 275 |
| Uniform Distribution, U(a, b) | p. 275 |
| Normal (Gaussian) Distribution, N(¿, ¿) | p. 275 |
| Lognormal Distribution, LN(¿, ¿) | p. 275 |
| t Distribution, T(¿, ¿, ¿2) | p. 276 |
| Gamma Distribution, Gamma(¿, ß) | p. 276 |
| Weibull Distribution, Weibulla(¿, ß) | p. 276 |
| Pareto Distribution (One-Parameter), Pareto(¿, x0) | p. 277 |
| Pareto Distribution (Two-Parameter), Pareto2(¿, ß) | p. 277 |
| Generalised Pareto Distribution, GPD(¿, ß) | p. 278 |
| Beta Distribution, Beta(¿, ß) | p. 278 |
| Generalised Inverse Gaussian Distribution, GIG(¿, ¿, ¿) | p. 279 |
| d-variate Normal Distribution, Nd(¿, ¿) | p. 280 |
| d-variate t-Distribution, Td(¿, ¿, ¿) | p. 280 |
| Selected Simulation Algorithms | p. 281 |
| Simulation from GIG Distribution | p. 281 |
| Simulation from ¿-stable Distribution | p. 282 |
| Solutions for Selected Problems | p. 283 |
| References | p. 289 |
| Index | p. 299 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9783642159220
ISBN-10: 3642159222
Published: 21st January 2011
Format: Hardcover
Language: English
Number of Pages: 322
Audience: Professional and Scholarly
Publisher: Springer Nature B.V.
Country of Publication: DE
Dimensions (cm): 22.86 x 15.88 x 2.54
Weight (kg): 0.58
Shipping
| Standard Shipping | Express Shipping | |
|---|---|---|
| Metro postcodes: | $9.99 | $14.95 |
| Regional postcodes: | $9.99 | $14.95 |
| Rural postcodes: | $9.99 | $14.95 |
Orders over $79.00 qualify for free shipping.
How to return your order
At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.
Additional postage charges may be applicable.
Defective items
If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.
For more info please visit our Help Centre.

























