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meteorological elements, Quarterly Journal of the Royal Meteorological Society, Vol. 87, 1955,
pp. 145“58.
APPENDIX 5
Chat¬eld C. and Collins A. J., Introduction to Multivariate Analysis, Chapman & Hall, 1980.
Saporta G., Probabilit´ s, Analyse des Donn´ es et Statistique, Technip, 1990.
e e

APPENDIX 6
Chat¬eld C. and Collins A. J., Introduction to Multivariate Analysis, Chapman & Hall, 1980.
Saporta G., Probabilit´ s, Analyse des Donn´ es et Statistique, Technip, 1990.
e e

APPENDIX 7
Droesbeke J. J., Fichet B., and Tassi P, Mod´ lisation ARCH, th´ rine statistique et applications dans
e e
´
le domaine de la ¬nance, Editions ULB, 1994.
Engel R. F., Auto-regressive conditional heteroscedasticity with estimate of the variance of United
Kingdom in¬‚ation, Econometrica, No. 50, 1982, pp. 987“1003.
Gourieroux C., Mod` les ARCH et applications ¬nanci` res, Economica, 1992.
e e
Nelson D. B., Conditional heteroscedasticity in asset returns: a new approach, Econometrica, No.
39, 1991, pp. 347“70.
APPENDIX 8
Burden R. L. and Faires D. J., Numerical Analysis, Prindle, Weber & Schmidt, 1981.
Litt F. X., Analyse num´ rique, premi` re partie, ULG, 1999.
e e
Nougier J-P., M´ thods de calcul num´ rique, Masson, 1993.
e e

INTERNET SITES
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http://www.iasc.org.uk/cmt/0001.asp
http://www.ifac.org
http://www.prim.lu
Index

absolute global risk 285 autoregressive integrated moving average
320
absolute risk aversion coef¬cient 88
autoregressive moving average (ARMA) 318
accounting standards 9“10
average deviation 41
accrued interest 118“19
actuarial output rate on issue 116“17
actuarial return rate at given moment 117 bank offered rate (BOR) 305
adjustment tests 361 basis point 127
Aitken extrapolation 376 Basle Committee for Banking Controls 4
Akaike™s information criterion (AIC) 319 Basle Committee on Banking Supervision
allocation 3“9
Basle II 5“9
independent allocation 288
Bayesian information criterion (BIC) 319
joint allocation 289
bear money spread 177
of performance level 289“90
benchmark abacus 287“8
of systematic risk 288“9
Bernouilli scheme 350
American option 149
Best Linear Unbiased Estimators (BLUE) 363
American pull 158“9
beta
arbitrage 31
APT 290, 291
arbitrage models 138“9
portfolio 92
with state variable 139“42
bijection 335
arbitrage pricing theory (APT) 97“8,
binomial distribution 350“1
99
binomial formula (Newton™s) 111, 351
absolute global risk 285
binomial law of probability 165
analysis of style 291“2
binomial trees 110, 174
beta 290, 291
binomial trellis for underlying equity 162
factor-sensitivity pro¬le 285
bisection method 380
model 256, 285“94 Black and Scholes model 33, 155, 174, 226,
relative global risk/tracking error 285“7 228, 239
ARCH 320 for call option 169
ARCH-GARCH models 373 dividends and 173
arithmetical mean 36“7 for options on equities 168“73
ARMA models 318“20 sensitivity parameters 172“3
asset allocation 104, 274 BLUE (Best Linear Unbiased Estimators) 363
asset liability management bond portfolio management strategies 135“8
replicating portfolios 311“21 active strategy 137“8
repricing schedules 301“11 duration and convexity of portfolio 135“6
simulations 300“1 immunizing a portfolio 136“7
structural risk analysis in 295“9 positive strategy: immunisation 135“7
VaR in 301 bonds
autocorrelation test 46 average instant return on 140
390 Index
bonds (continued ) convergence 375“6
de¬nition 115“16 convertible bonds 116
¬nancial risk and 120“9 convexity 33, 149, 181
price 115 of a bond 127“9
price approximation 126 corner portfolio 64
return on 116“19 correlation 41“2, 346“7
sources of risk 119“21 counterparty 23
valuing 119 coupon (nominal) rate 116
bootstrap method 233 coupons 115
Brennan and Schwarz model 139 covariance 41“2, 346“7
building approach 316 cover law of probability 164
bull money spread 177 Cox, Ingersoll and Ross model 139, 145“7,
business continuity plan (BCP) 14 174
insurance and 15“16 Cox, Ross and Rubinstein binomial model
operational risk and 16 162“8
origin, de¬nition and objective 14 dividends and 168
butter¬‚y money spread 177 one period 163“4
T periods 165“6
two periods 164“5
calendar spread 177 credit risk 12, 259
call-associated bonds 120 critical line algorithm 68“9
call option 149, 151, 152
intrinsic value 153
premium breakdown 154 debentures 18
call“put parity relation 166 decision channels 104, 105
for European options 157“8 default risk 120
canonical analysis 369 de¬cit constraint 90
canonical correlation analysis 307“9, degenerate random variable 341
369“70 delta 156, 181, 183
capital asset pricing model (CAPM or delta hedging 157, 172
MEDAF) 93“8 derivatives 325“7
equation 95“7, 100, 107, 181 calculations 325“6
cash 18 de¬nition 325
catastrophe scenarios 20, 32, 184, 227 extrema 326“7
Cauchy™s law 367 geometric interpretations 325
central limit theorem (CLT) 41, 183, 223, determinist models 108“9
348“9 generalisation 109
Charisma 224 stochastic model and 134“5
Chase Manhattan 224, 228 deterministic structure of interest rates
Choleski decomposition method 239 129“35
Choleski factorisation 220, 222, development models 30
336“7 diagonal model 70
chooser option 176 direct costs 26
chord method 377“8 dirty price 118
classic chord method 378 discrete models 30, 108, 109“11. 130,
clean price 118 132“4
collateral management 18“19 discrete random variables 340“1
compliance 24 dispersion index 26
compliance tests 361 distortion models 138
compound Poisson process 355 dividend discount model 104, 107“8
conditional normality 203 duration 33, 122“7, 149
con¬dence coef¬cient 360 and characteristics of a bond 124
con¬dence interval 360“1 de¬nition 121
continuous models 30, 108“9, 111“13, extension of concept of 148
131“2, 134 interpretations 121“3
continuous random variables 341“2 of equity funds 299
contract-by-contract 314“16 of speci¬c bonds 123“4
Index 391
dynamic interest-rate structure 132“4 exchange risk 12
exercise price of option 149
dynamic models 30
expected return 40
dynamic spread 303“4
expected return risk 41, 43
expected value 26
ef¬ciency, concept of 45 exponential smoothing 318
ef¬cient frontier 27, 54, 59, 60 extrema 326“7, 329“31
for model with risk-free security 78“9 extreme value theory 230“4, 365“7
for reformulated problem 62 asymptotic results 365“7
for restricted Markowitz model 68 attraction domains 366“7
for Sharpe™s simple index model 73 calculation of VaR 233“4
unrestricted and restricted 68 exact result 365
ef¬cient portfolio 53, 54 extreme value theorem 230“1
EGARCH models 320, 373 generalisation 367
elasticity, concept of 123 parameter estimation by regression 231“2
Elton, Gruber and Padberg method 79“85, parameter estimation using the
265, 269“74 semi-parametric method 233, 234
adapting to VaR 270“1
cf VaR 271“4
factor-8 mimicking portfolio 290
maximising risk premium 269“70
factor-mimicking portfolios 290
equities
factorial analysis 98
de¬nition 35
fair value 10
market ef¬ciency 44“8
fat tail distribution 231
market return 39“40
festoon effect 118, 119
portfolio risk 42“3
¬nal prediction error (FPE) 319
return on 35“8
Financial Accounting Standards Board (FASB)
return on a portfolio 38“9
9
security risk within a portfolio 43“4
¬nancial asset evaluation line 107
equity capital adequacy ratio 4
¬rst derivative 325
equity dynamic models 108“13
Fisher™s skewness coef¬cient 345“6
equity portfolio diversi¬cation 51“93
¬xed-income securities 204
model with risk-free security 75“9
¬xed-rate bonds 115
portfolio size and 55“6
¬xed rates 301
principles 515
¬‚oating-rate contracts 301
equity portfolio management strategies 103“8
¬‚oating-rate integration method 311
equity portfolio theory 183
FRAs 276
equity valuation models 48“51
Fr´ chet™s law 366, 367
e
equivalence, principle of 117
frequency 253
ergodic estimator 40, 42
fundamental analysis 45
estimated variance“covariance matrix method
(VC) 201, 202“16, 275, 276, 278
breakdown of ¬nancial assets 203“5 gamma 156, 173, 181, 183
calculating VaR 209“16 gap 296“7, 298
hypotheses and limitations 235“7 GARCH models 203, 320
installation and use 239“41 Garman“Kohlhagen formula 175
mapping cash¬‚ows with standard maturity Gauss-Seidel method, nonlinear 381
dates 205“9 generalised error distribution 353
valuation models 237“9 generalised Pareto distribution 231
estimator for mean of the population 360 geometric Brownian motion 112, 174, 218,
European call 158“9 237, 356
European option 149 geometric mean 36
event-based risks 32, 184 geometric series 123, 210, 328“9
ex ante rate 117 global portfolio optimisation via VaR 274“83
ex ante tracking error 285, 287 generalisation of asset model 275“7
ex post return rate 121 construction of optimal global portfolio
exchange options 174“5 277“8
exchange positions 204 method 278“83
392 Index
good practices 6 models for bonds 149
Gordon “ Shapiro formula 48“50, 107, 149 static structure of 130“2
government bonds 18 internal audit vs. risk management 22“3
Greeks 155“7, 172, 181 internal notation (IN) 4
gross performance level and risk withdrawal intrinsic value of option 153
290“1 Itˆ formula (Ito lemma) 140, 169, 357
o
Gumbel™s law 366, 367 Itˆ process 112, 356
o

Heath, Jarrow and Morton model 138, 302 Jensen index 102“3
hedging formula 172 Johnson distributions 215
Hessian matrix 330 joint allocation 289
high leverage effect 257 joint distribution function 342
Hill™s estimator 233
historical simulation 201, 224“34, 265
kappa see vega
basic methodology 224“30
kurtosis coef¬cient 182, 189, 345“6
calculations 239
data 238“9
Lagrangian function 56, 57, 61, 63, 267,
extreme value theory 230“4
331
hypotheses and limitations 235“7
for risk-free security model 76
installation and use 239“41
for Sharpe™s simple index model 71
isolated asset case 224“5
Lagrangian multipliers 57, 331
portfolio case 225“6
law of large numbers 223, 224, 344
risk factor case 224
law of probability 339
synthesis 226“30
least square method 363
valuation models 237“8
legal risk 11, 21, 23“4
historical volatility 155
Lego approach 316
histories 199
leptokurtic distribution 41, 182, 183, 189,
Ho and Lee model 138
218, 345
homogeneity tests 361
linear equation system 335“6
Hull and White model 302, 303
linear model 32, 33, 184
hypothesis test 361“2
linearity condition 202, 203
Lipschitz™s condition 375“6
IAS standards 10
liquidity bed 316
IASB (International Accounting Standards
liquidity crisis 17
Board) 9
liquidity preference 316
IFAC (International Federation of Accountants)
liquidity risk 12, 16, 18, 296“7
9
logarithmic return 37
immunisation of bonds 124“5
logistic regression 309“10, 371
implied volatility 155
log-normal distribution 349“50
in the money 153, 154
log-normal law with parameter 349
independence tests 361
long (short) straddle 176
independent allocation 288
loss distribution approach 13
independent random variables 342“3
lottery bonds 116
index funds 103
indifference curves 89
MacLaurin development 275, 276
indifference, relation of 86
mapping cash¬‚ows 205“9
indirect costs 26
according to RiskMetricsT M 206“7
inequalities on calls and puts 159“60
alternative 207“8
inferential statistics 359“62
elementary 205“6
estimation 360“1
marginal utility 87
sampling 359“60
market ef¬ciency 44“8
sampling distribution 359“60
market model 91“3
instant term interest rate 131
market price of the risk 141
integrated risk management 22, 24“5
market risk 12
interest rate
market straight line 94
curves 129
Index 393
market timing 104“7 solving 375“81
nonlinear Gauss-Seidel method 381
Markowitz™s portfolio theory 30, 41, 43,
nonlinear models independent of time 33
56“69, 93, 94, 182
nonlinear regression 234
¬rst formulation 56“60
non-quanti¬able risks 12“13
reformulating the problem 60“9
normal distribution 41, 183, 188“90, 237,
mathematic valuation models 199
254, 347“8
matrix
normal law 188
algebra 239
normal probability law 183
calculus 332“7
normality 202, 203, 252“4
diagonal 333
n-order 332
operations 333“4 observed distribution 254
symmetrical 332“3, 334“5 operational risk 12“14
maturity price of bond 115 business continuity plan (BCP) and 16
maximum out¬‚ow 17“18 de¬nition 6
mean 343“4 management 12“13
mean variance 27, 265 philosophy of 5“9
for equities 149 triptych 14
measurement theory 344 options
media risk 12 complex 175“7
Merton model 139, 141“2 de¬nition 149
minimum equity capital requirements 4 on bonds 174
modern portfolio theory (MPT) 265 sensitivity parameters 155“7
modi¬ed duration 121 simple 175
money spread 177 strategies on 175“7
monoperiodic models 30 uses 150“2
Monte Carlo simulation 201, 216“23, 265, value of 153“60
303 order of convergence 376
calculations 239 Ornstein “ Uhlenbeck process 142“5, 356
data 238“9 OTC derivatives market 18
estimation method 218“23 out of the money 153, 154
hypotheses and limitations 235“7 outliers 241
installation and use 239“41
probability theory and 216“18
Pareto distribution 189, 367
synthesis 221“3
Parsen CAT 319
valuation models 237“8
partial derivatives 329“31
multi-index models 221, 266
payment and settlement systems 18
multi-normal distribution 349
Pearson distribution system 183
multivariate random variables 342“3
perfect market 31, 44
mutual support 147“9
performance evaluation 99“108
perpetual bond 123“4
Nelson and Schaefer model 139 Picard™s iteration 268, 271, 274, 280, 375,
net present value (NPV) 298“9, 302“3 376, 381
neutral risk 164, 174 pip 247
New Agreement 4, 5 pockets of inef¬ciency 47
Newson“Raphson nonlinear iterative method Poisson distribution 350
309, 379“80, 381 Poisson process 354“5
Newton™s binomial formula 111, 351 Poisson™s law 351
nominal rate of a bond 115, 116 portfolio beta 92
nominal value of a bond 115 portfolio risk management
non-correlation 347 investment strategy 258
nonlinear equation systems 380“1 method 257“64
¬rst-order methods 377“9 risk framework 258“64
iterative methods 375“7 power of the test 362
n-dimensional iteration 381 precautionary surveillance 3, 4“5
principal methods 381 preference, relation of 86
394 Index
premium 149 function, purpose of 11
price at issue 115 methodology 19“21
price-earning ratio 50“1 vs back of¬ce 22
price of a bond 127 risk mapping 8
price variation risk 12 risk measurement 8, 41
probability theory 216“18 risk-neutral probability 162, 164
process risk 24 risk neutrality 87
product risk 23 risk of one equity 41
pseudo-random numbers 217 risk of realisation 120
put option 149, 152 risk of reinvestment 120
risk of reputation 21
risk per share 181“4
quadratic form 334“7
risk premium 88
qualitative approach 13
risk return 26“7
quanti¬able risks 12, 13
risk transfer 14
quantile 188, 339“40
risk typology 12“19
quantitative approach 13
Risk$TM 224, 228
RiskMetricsTM 202, 203, 206“7, 235, 236,
Ramaswamy and Sundaresan model 238, 239“40
139
random aspect of ¬nancial assets 30
scenarios and stress testing 20
random numbers 217
Schaefer and Schwartz model 139
random variables 339“47
Schwarz criterion 319
random walk 45, 111, 203, 355
scope of competence 21
statistical tests for 46
scorecards method 7, 13
range forwards 177
security 63“5
rate ¬‚uctuation risk 120
security market line 107
rate mismatches 297“8
self-assessment 7
rate risk 12, 303“11
semi-form of ef¬ciency hypothesis
redemption price of bond 115
46
regression line 363
semi-parametric method 233
regressions 318, 362“4
semi-variance 41
multiple 363“4
sensitivity coef¬cient 121
nonlinear 364
separation theorem 94“5, 106
simple 362“3
series 328
regular falsi method 378“9
Sharpe™s multi-index model 74“5
relative fund risk 287“8
Sharpe™s simple index method 69“75,
relative global risk 285“7
100“1, 132, 191, 213, 265“9
relative risks 43
adapting critical line algorithm to VaR
replicating portfolios 302, 303,
267“8
311“21
cf VaR 269
with optimal value method 316“21
for equities 221
repos market 18
problem of minimisation
repricing schedules 301“11
266“7
residual risk 285
VaR in 266“9
restricted Markowitz model 63“5
short sale 59
rho 157, 173, 183
Richard model 139 short-term interest rate 130
risk, attitude towards 87“9 sign test 46
risk aversion 87, 88 simulation tests for technical analysis methods
risk factors 31, 184 46
risk-free security 75“9 simulations 300“1
risk, generalising concept 184 skewed distribution 182
risk indicators 8 skewness coef¬cient 182, 345“6
risk management speci¬c risk 91, 285
cost of 25“6 speculation bubbles 47
environment 7 spot 247
Index 395
spot price 150 time value of option 153, 154
spot rate 129, 130 total risk 43
spreads 176“7 tracking errors 103, 285“7
square root process 145 transaction risk 23“4
St Petersburg paradox 85 transition bonds 116
standard Brownian motion 33, 355 trend extrapolations 318
standard deviation 41, 344“5 Treynor index 102
standard maturity dates 205“9 two-equity portfolio 51“4
standard normal law 348
static models 30
static spread 303“4
unbiased estimator 360
stationarity condition 202, 203, 236
underlying equity 149
stationary point 327, 330
uniform distribution 352
stationary random model 33
uniform random variable 217
stochastic bond dynamic models
utility function 85“7
138“48
utility of return 85
stochastic differential 356“7
utility theory 85“90, 183
stochastic duration 121, 147“8
random evolution of rates 147
stochastic integral 356“7
stochastic models 109“13 valuation models 30, 31“3, 160“75, 184
stochastic process 33, 353“7 value at risk (VaR) 13, 20“1
particular 354“6 based on density function 186
path of 354 based on distribution function 185
stock exchange indexes 39 bond portfolio case 250“2
stock picking 104, 275 breaking down 193“5
stop criteria 376“7 calculating 209“16
stop loss 258“9 calculations 244“52
straddles 175, 176 component 195
strangles 175, 176 components of 195
strategic risk 21 de¬nition 195“6
stress testing 20, 21, 223 estimation 199“200
strike 149 for a portfolio 190“7
strike price 150 for a portfolio of linear values 211“13
strong form of ef¬ciency hypothesis 46“7 for a portfolio of nonlinear values
Student distribution 189, 235, 351“2 214“16
Student™s law 367 for an isolated asset 185“90
Supervisors, role of 8 for equities 213“14
survival period 17“18 heading investment 196“7
systematic inef¬ciency 47 incremental 195“7
systematic risk 44, 91, 285 individual 194
allocation of 288“9 link to Sharp index 197
marginal 194“5
maximum, for portfolio 263“4
tail parameter 231
normal distribution 188“90
taste for risk 87
Treasury portfolio case 244“9
Taylor development 33, 125, 214, 216,
typology 200“2
275“6
value of basis point (VBP) 19“20, 21, 127,
Taylor formula 37, 126, 132, 327“8,
245“7, 260“3
331
variable contracts 301
technical analysis 45
variable interest rates 300“1
temporal aspect of ¬nancial assets 30
variable rate bonds 115
term interest rate 129, 130
variance 41, 344“5
theorem of expected utility 86
variance of expected returns approach 183
theoretical reasoning 218
variance “ covariance matrix 336
theta 156, 173, 183
Vasicek model 139, 142“4, 174
three-equity portfolio 54
396 Index
vega (kappa) 156, 173 yield curve 129
volatility of option 154“5 yield to maturity (YTM) 250

weak form of the ef¬ciency hypothesis 46 zero-coupon bond 115, 123, 129
Weibull™s law 366, 367 zero-coupon rates, analysis of correlations on
Wiener process 355 305“7


Index compiled by Annette Musker

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. 16
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