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

More documents

Recommendations

Info

and gave their support to this long-term effort over the years since April 2006. The members of the steering committee have been a great support for this endeavour. We want to particularly thank Andy Zdrenyk and Paolo de Martin whose strong support reflected the importance of this documentation for the entire company. Last but not least, we would like to point out the two project managers who accompanied us along these months with their commitment and dedication through all the ups and downs of such a demanding project: Jindrich Wagner and Viviane Engelmayer. You all made this project possible and gave us a sense of pride for the development of our internal model and its enhancements that will ultimately allow us to fulfil the regulators’ requirements. Michel Dacorogna Head of Group Financial Modeling SCOR Group ix April, 2008
List of Contributors NAME FUNCTION COMPANY Blum Peter Research Associate SCOR Bürgi Roland Senior Risk Consultant SCOR Dacorogna Michel Head of Financial Modeling SCOR de Braaf Karsten Life Actuary SCOR Dossena Miriam Risk Consultant SCOR Engelmayer Viviane SST Project Manager SCOR Erixon Erik Consultant Towers Perrin Gallati Livia Legal Counsel SCOR Gose Bernhard Consultant Towers Perrin Grützner Guido Life Actuary SCOR Gut Markus Documentation Editor SCOR Heil Jan Investment Controller SCOR Homrighausen Jost Life Actuary SCOR Hummel Christoph Actuarial Risk Modeling SCOR Iannuzzi Debora Risk Consultant SCOR Jäger Markus Life Actuary and Risk Manager SCOR Kalberer Tigran Principal Towers Perrin Küttel Stefan Head of Pricing Zurich & Cologne SCOR Langer Bernd Chief Risk Officer Global P&C SCOR Matter Flavio Cat Risk Analyst SCOR Möhr Christoph Actuarial Risk Modeling SCOR Moller Michael Senior Risk Consultant SCOR Müller Ulrich Senior Risk Consultant SCOR Pabst Brigitte Cat Risk Analyst SCOR Rüttener Erik Head of Natural Hazards SCOR x
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 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 22 and 23: 3.9.4 Dependency Structure and Aggr
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?