From Principle-Based Risk Management to Solvency ... - Scor

More documents

Recommendations

Info

3.9.4 Dependency Structure and Aggregation for Run-Off Business.......................... 99 3.9.5 Data Requirements and Parameter for Run-Off Business..........................100 3.10 Model for Non-Life Internal Administrative Expenses . . . . . 3.10.1AcquisitionandMaintenanceCosts...........101 100 3.10.2 Required Data and Discussion . . . ..........103 4 Life and Health Methodology 104 4.1StructureoftheBusiness ....................104 4.2GMDB...............................106 4.3FinanceRe ............................108 4.3.1DefinitionandExposure.................108 4.3.2 Stochastic Modeling . . .................108 4.3.3DependencyStructure..................109 4.4TrendRisk ............................109 4.4.1DefinitionandExposure.................109 4.4.2 Stochastic Modeling . . .................110 4.4.3ChoiceofParameters ..................110 4.4.4DependencyStructure..................111 4.4.5 Cash Flow Modeling . . .................111 4.5FluctuationRisk .........................111 4.5.1DefinitionandExposure.................111 4.5.2 Stochastic Modeling . . .................112 4.5.3DeterminationofRiskClusters.............115 4.5.4ChoiceofParameters ..................117 4.5.5 Technical Modeling . . . .................120 4.6 Dependency Structure of the Risk-Categories . . . . . . . . . 120 4.7 The GMDB Replicating Portfolio . . . . . . ..........121 4.7.1 Determining a Set of Replicating Assets . . . . . . . . 124 4.7.2 Calibration of the Replicating Portfolio . . . . . . . . 131 4.7.3CheckingandBias ....................133 4.7.4 Projecting the Replicating Portfolio ..........135 4
5 Dependency Structure of the Life & Health Insurance Risk with the Non-Life Insurance Risks 138 6 Mitigation of Insurance Risk 140 7 Limitations of the Liability Model 143 7.1LifeBusiness ...........................143 7.2Non-LifeBusiness.........................143 7.2.1NewBusinessModel...................144 7.2.2 Natural Catastrophe Modeling . . . ..........145 7.2.3Run-offBusinessModel .................146 8 Appendix 148 8.1PortfolioDependencyTree....................148 8.1.1SuitablePortfolioDecomposition............148 8.1.2 Why Suitability is Needed . . . . . . ..........150 8.2 Modeling Dependencies .....................152 8.2.1 Explicit and Implicit Dependency Models . . . . . . . 153 8.2.2Copulas ..........................154 8.2.3 Linear Correlation and other Dependency Measures . 158 8.2.4ArchimedeanCopulas,ClaytonCopula.........161 8.2.5 Explicit Dependency between Economic Variables and Liabilities .........................165 8.3 Pricing Capital Allocation . . . .................168 8.3.1Introduction .......................169 8.3.2 Preliminaries . . .....................172 8.3.3 Risk Measure, Capital Allocation, Euler Principle, Risk Function..........................173 8.3.4 Capital Allocation for a Portfolio Dependency Tree . . 180 8.3.5TemporalityofCapital,CapitalCosts .........185 8.3.6 Sufficient premium, Performance excess, RAC, TRAC 186 5
Page 1 and 2: From Principle-Based Risk Managemen
Page 3: Table of Contents Prefaces iv Ackno
Page 6 and 7: I shall not go into the different c
Page 8 and 9: cate the capital necessary for the
Page 10 and 11: and gave their support to this long
Page 12 and 13: NAME FUNCTION COMPANY Schindler Chr
Page 14 and 15: approach. The major risk factor cat
Page 16 and 17: force”), the volatility clusterin
Page 18 and 19: Part IX gives an outlook on the cur
Page 20 and 21: Table of Contents 1 Preliminaries 8
Page 24 and 25: List of Tables 3.1 The portfolio de
Page 26 and 27: 1 Preliminaries Financial instrumen
Page 28 and 29: 2.1 Basics of Valuation 2.1.1 Valua
Page 30 and 31: has been removed. In the option exa
Page 32 and 33: Different types of “imperfect rep
Page 34 and 35: only depends on the law, i.e. the d
Page 36 and 37: For this reason, we define an unbia
Page 38 and 39: value of the assets has to exceed t
Page 40 and 41: educes the amounts Ki and thus the
Page 42 and 43: Hence, basis risk arises when the a
Page 44 and 45: � the default option � sharehol
Page 46 and 47: Note that the set Ω⋆ 1 exclude t
Page 48 and 49: In view of the solvency condition (
Page 50 and 51: that year. The change in the estima
Page 52 and 53: The “stand-alone” shortfalls ES
Page 54 and 55: Further, we propose to calculate th
Page 56 and 57: We propose the following treatment
Page 58 and 59: In pricing, on the other hand, the
Page 60 and 61: We distinguish within the non-life
Page 62 and 63: To be more precise, a model is cons
Page 64 and 65: conditional on the information avai
Page 66 and 67: not for run-off business. The propo
Page 68 and 69: � Dependency between new, prior-y
Page 70 and 71: Run-Off Business By definition, run
Page 72 and 73:
3.2.4 New Business, Prior-Year Busi
Page 74 and 75:
� Run-off business model for the
Page 76 and 77:
� Basket specific models: In thes
Page 78 and 79:
Agribusiness (θ =0.2673) Marine (
Page 80 and 81:
Basket Specific Models Basket speci
Page 82 and 83:
is reasonable and, in particular, c
Page 84 and 85:
Credit and Surety (Section 3.6, pp.
Page 86 and 87:
An alternative approach is used, fo
Page 88 and 89:
Historical losses are “as if” a
Page 90 and 91:
In general, the structure of a rein
Page 92 and 93:
� Measures of profitability such
Page 94 and 95:
affected airlines respectively manu
Page 96 and 97:
Note that for the exposure loss mod
Page 98 and 99:
3.7.4 Simulation Currently it is no
Page 100 and 101:
with the modeling of the hazard, th
Page 102 and 103:
3.8.2 Hazard Module Wind Windstorm
Page 104 and 105:
ical source zones as fault, area or
Page 106 and 107:
exposure retrieval and preparation,
Page 108 and 109:
areas. Catrader performs analyzes o
Page 110 and 111:
� paid external expenses (brokera
Page 112 and 113:
� underwriting years k =0, 1 ...,
Page 114 and 115:
� Volatility in the Mack model co
Page 116 and 117:
the mean-squared error for the one-
Page 118 and 119:
3.9.5 Data Requirements and Paramet
Page 120 and 121:
where we might take ai =(1+θ) i fo
Page 122 and 123:
4 Life and Health Methodology Our d
Page 124 and 125:
4.2 GMDB Definition and Exposure Th
Page 126 and 127:
4.3 Finance Re 4.3.1 Definition and
Page 128 and 129:
are almost not affected by changes
Page 130 and 131:
Fluctuation risk should be seen in
Page 132 and 133:
Probability 10 x 10-4 Number of cla
Page 134 and 135:
� Geography � Product types �
Page 136 and 137:
� Determination of the frequency
Page 138 and 139:
� Industry accident (contaminatio
Page 140 and 141:
scenarios used, the same economic s
Page 142 and 143:
4.7.1 Determining a Set of Replicat
Page 144 and 145:
need to be evaluated is small compa
Page 146 and 147:
Asset Strike Number of assets Europ
Page 148 and 149:
Figure 4.4: Surface plot of GMDB ca
Page 150 and 151:
Figure 4.7: GMDB with no maximum fo
Page 152 and 153:
Standard deviation 400 000 350 000
Page 154 and 155:
formula both including and excludin
Page 156 and 157:
5 Dependency Structure of the Life
Page 158 and 159:
6 Mitigation of Insurance Risk This
Page 160 and 161:
We compute the two parameters which
Page 162 and 163:
usiness written in the first year i
Page 164 and 165:
For multi-location policies the qua
Page 166 and 167:
8 Appendix 8.1 Portfolio Dependency
Page 168 and 169:
Z1,1 Z1,1,1 Z1,1,2 Z1 Z1,2 Z1,3 Z Z
Page 170 and 171:
To this probability, suitability (8
Page 172 and 173:
insurance losses gives the insured
Page 174 and 175:
Moreover, the copula C is given by
Page 176 and 177:
continuous margins F1 and F2 and ex
Page 178 and 179:
The third fallacy pertains to corre
Page 180 and 181:
function C :[0, 1] d → [0, 1] has
Page 182 and 183:
The d-dimensional Clayton copula is
Page 184 and 185:
The two stochastic variables X and
Page 186 and 187:
3. Use Equation (8.19) to compute t
Page 188 and 189:
usiness and type of business, the e
Page 190 and 191:
Further approaches to capital alloc
Page 192 and 193:
(Xi)i=1,...,m, so for the net prese
Page 194 and 195:
e a bounded, monotonously decreasin
Page 196 and 197:
Definition 8.5 The composition C⋆
Page 198 and 199:
in the portfolio. According to (8.5
Page 200 and 201:
Now assume that H0 is an arbitrary
Page 202 and 203:
Definition 8.13 For a copula C, the
Page 204 and 205:
consequently, the total capital cos
Page 206 and 207:
The time factor τX1+X2 of the sum
Page 208 and 209:
where the probability measure GX,Z
Page 210 and 211:
II Market Risk 192
Page 212 and 213:
10.3.8 Interaction and Expectation
Page 214 and 215:
List of Tables 12.1 Approximation f
Page 216 and 217:
9 Introduction 9.1 Economic Risks i
Page 218 and 219:
vations by means of statistical res
Page 220 and 221:
the details needed in any concrete
Page 222 and 223:
lation of future time intervals. Wh
Page 224 and 225:
10.2 Bootstrapping - the Method and
Page 226 and 227:
value 3 : xj = Ej−1[xj]+Ii (10.4)
Page 228 and 229:
generation of the underlying econom
Page 230 and 231:
this behavior conforms to theory an
Page 232 and 233:
Calibrating the parameters of a GAR
Page 234 and 235:
where u is a uniformly distributed
Page 236 and 237:
� Do we use the same random varia
Page 238 and 239:
example from 15 March 2007 to 15 Ju
Page 240 and 241:
This is Equation (10.3) applied to
Page 242 and 243:
The solid curve shows the mapping o
Page 244 and 245:
as no uncertainty on the outcome re
Page 246 and 247:
� Convert all ¯zj(T ) to the sim
Page 248 and 249:
is to subtract the mean of all hist
Page 250 and 251:
the basis of a study of the behavio
Page 252 and 253:
10.3.11 Equity Indices Many applica
Page 254 and 255:
Historical behaviors are reproduced
Page 256 and 257:
this. The discrepancy Φi(x) − ˆ
Page 258 and 259:
ate 15 against the USD, CPI and GDP
Page 260 and 261:
10.5 Conclusion Refined bootstrappi
Page 262 and 263:
we do not choose a time constant ex
Page 264 and 265:
11 Interest Rate Hedges Under the d
Page 266 and 267:
a year), then the coupon C (annuali
Page 268 and 269:
11.5.2 Notes Inputs: � Notional (
Page 270 and 271:
ment bonds. Portfolios of bonds are
Page 272 and 273:
these are uniformly distributed ove
Page 274 and 275:
� The initial market value of the
Page 276 and 277:
FX rate, CTA acc init . In the Mell
Page 278 and 279:
and the target MTM (= ¯ T ) which
Page 280 and 281:
The coupon rate Cn of the new bond
Page 282 and 283:
12.9 Cash Flow from or to the Portf
Page 284 and 285:
In a multi-period simulation, the e
Page 286 and 287:
The sum of all book values equals t
Page 288 and 289:
calculations. The yield y ′ i of
Page 290 and 291:
After the external cash flow and th
Page 292 and 293:
investment. The two main categories
Page 294 and 295:
gains and losses is U acc final = U
Page 296 and 297:
of individual time steps as simple
Page 298 and 299:
The book value in accounting curren
Page 300 and 301:
13.7 Accounting Results in Local Cu
Page 302 and 303:
Another useful variable is the tota
Page 304 and 305:
study of that rate, we use an avera
Page 306 and 307:
14.2 Timing: The Simulation Period
Page 308 and 309:
2. The final asset component which
Page 310 and 311:
15 Foreign Exchange Risk 15.1 FX Ri
Page 312 and 313:
This is the factor we apply to esti
Page 314 and 315:
III Credit Risk 296
Page 316 and 317:
18.5 Modeling Credit Risks of a Rei
Page 318 and 319:
17 Introduction 17.1 Credit Risk in
Page 320 and 321:
Modeling credit spreads and default
Page 322 and 323:
isks are the most important ones, s
Page 324 and 325:
18.2 Variables to Describe Credit R
Page 326 and 327:
slowly reacting variable subject to
Page 328 and 329:
(18.3) by using some standard value
Page 330 and 331:
The likely yield Y (T ) of a bond i
Page 332 and 333:
of sector rotation. The market some
Page 334 and 335:
Now the dynamic model for X/C can b
Page 336 and 337:
and used by practitioners and which
Page 338 and 339:
observed dependence between credit
Page 340 and 341:
19 Limitations of the Credit Risk M
Page 342 and 343:
Table of Contents 20 Operational Ri
Page 344 and 345:
4. Incident Management, i.e. detect
Page 346 and 347:
V The Economic Balance Sheet 328
Page 348 and 349:
List of Tables 25.1 The classes of
Page 350 and 351:
22 Aggregating Risk Inputs to Balan
Page 352 and 353:
23 Legal Entities and Parental Guar
Page 354 and 355:
2. In August of 2004, in order to r
Page 356 and 357:
The asset-liability portfolio is co
Page 358 and 359:
ealize the economic value of this e
Page 360 and 361:
25 The Valuation of Assets The SST
Page 362 and 363:
Assets Valuation Fixed maturities I
Page 364 and 365:
with non-material value are taken a
Page 366 and 367:
Liability Valuation Underwriting re
Page 368 and 369:
VI Solvency Capital Requirements 35
Page 370 and 371:
VII Process Landscape 352
Page 372 and 373:
31.3 Roles and Responsibilities . .
Page 374 and 375:
List of Figures 29.1 Embedment of t
Page 376 and 377:
27 Summary The ultimate objective o
Page 378 and 379:
28 Structure of the Process Landsca
Page 380 and 381:
29 Overview 29.1 The Swiss Solvency
Page 382 and 383:
Process step Proposal for asset man
Page 384 and 385:
ALM Committee � Sign-off on adequ
Page 386 and 387:
30 The ALM Process 30.1 General Ove
Page 388 and 389:
Asset modeling: The asset portfolio
Page 390 and 391:
Inflation index The inflation in a
Page 392 and 393:
Simulate future time series Post pr
Page 394 and 395:
30.3.2 Reserve Modeling The purpose
Page 396 and 397:
Process Steps The following process
Page 398 and 399:
30.3.3 Liability Modeling The main
Page 400 and 401:
Retrocession Information on interna
Page 402 and 403:
Calculate gross reinsurance loss in
Page 404 and 405:
Unearned business modeler: The unea
Page 406 and 407:
Sign-off procedures Overall, the li
Page 408 and 409:
FX rates This data entity is taken
Page 410 and 411:
Roles and Responsibilities The role
Page 412 and 413:
Noninvested assets Balance sheet In
Page 414 and 415:
Financial controller � Provide da
Page 416 and 417:
31.2 Process Steps The following st
Page 418 and 419:
Risk management team ECS Scenario d
Page 420 and 421:
32 Appendix 32.1 Sign-off Matrix 32
Page 422 and 423:
Steering committee: Project sponsor
Page 424 and 425:
Function Body Responsible for Steer
Page 426 and 427:
Table of Contents 33 Summary 412 34
Page 428 and 429:
List of Tables 36.1 Economic variab
Page 430 and 431:
33 Summary This Part of the documen
Page 432 and 433:
and Bloomberg. One of the purposes
Page 434 and 435:
35 Architecture of SST Relevant Sys
Page 436 and 437:
35.1.2 Application Change Managemen
Page 438 and 439:
35.3 Revision Control The key to ga
Page 440 and 441:
IT SYSTEM DATA BASE DOCUMENT, DATA
Page 442 and 443:
Entity Time series used Risk-free y
Page 444 and 445:
Application FED User Bloomberg Othe
Page 446 and 447:
For investment indices, there is al
Page 448 and 449:
The initial data to the module are
Page 450 and 451:
module� data�input liability�
Page 452 and 453:
GCDP Aggregation of event losses MA
Page 454 and 455:
36.4.6 Planning and Business Projec
Page 456 and 457:
in Igloo and are used in conjunctio
Page 458 and 459:
flows for this simulation step. The
Page 460 and 461:
37 Architecture of New Developments
Page 462 and 463:
changing dimensions: Codes such as
Page 464 and 465:
each method has a corresponding set
Page 466 and 467:
38 Appendix We list the IT systems
Page 468 and 469:
IX Final Remarks 450
Page 470 and 471:
Acronyms A AAD Annual aggregate ded
Page 472 and 473:
L LE Legal entity. LGD Loss given d
Page 474 and 475:
Index Accident and health model bas
Page 476 and 477:
economic variables, 218-235 equity
Page 478 and 479:
invested assets and credit risk, 30
Page 480 and 481:
detrending, 211 economic variables,
Page 482 and 483:
Life & Health business, 105 Foreign
Page 484 and 485:
ing first development year, 63 occu
Page 486 and 487:
etrocession, 332-341 retrocession a
Page 488 and 489:
finance re, see Financial reinsuran
Page 490 and 491:
terest rate, 200 inflation, seasona
Page 492 and 493:
dependency structure with life and
Page 494 and 495:
Purchase guarantee, see liquidity a
Page 496 and 497:
Shareholder equity one year max cov
Page 498 and 499:
natural catastrophe modeling, 88 Vu
Page 500 and 501:
Bürgi, R. (2007). ALM Information
Page 502 and 503:
Gencyilmaz, C. (2007). Swiss Solven
Page 504 and 505:
Müller, U. A. (2007b). Modeling cr
show all

From Principle-Based Risk Management to Solvency ... - Scor

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?