Index

acceptable portfolios 23, 25–6 asymmetries analysis 342–5 accumulated value 77–83 asymptotic MEWMA control charts advanced measurement approach 251, 253, 254–8 (AMA) 2 atomic simulation 165 calibration 12–16 augmented Dickey–Fuller (ADF) test aggregate desirability of a portfolio 307 29–30 Australia 328 Agrawal, D. 108 autocorrelation 339 Akhavein, J. 109 autoregressive models 48 α-stable distributions 146–50 NPV probability distribution and α-stable intensity-based model autoregressive cash flows 286–7, 148–50 288, 289–93, 297–301 properties of the family 146–7 average run lengths (ARLs) 247, 254, simulation 147–8 255–8 American Depository Receipts (ADRs) average stock risk 108–9 305 Andersen, L. 354 Andersen, T.G. 115, 246 Bachelier, L. 194 Andersson, E. 242 backtesting 200 Andreasen, J. 354 VaR models 214–17 approximations, models as 198 backward-looking models 200 Aragó, V. 304 Balkema, A.A. 7 Aramov, D. 108 bankruptcy, probability of 283–4 arbitrage models 92 Basel Committee on Banking ARCH models 48, 86–7 Supervision 1 conditional 89–91 Basel II framework 1–2, 8 ARCH test 306–7 basic indicator approach (BIA) 2 Artzner, P. 22, 24–5, 27, 28 basic multivariate normal (BMVN) asymmetric covariance 328–9, 348, method 161–8 349–50, 351 accurate estimation of correlation asymmetric dynamic covariance matrix 162–3 (ADM) model 329–51 consistency between valuation of asymmetric volatility 328–9, 348, single contracts and portfolios 349–50, 351 166–7 asymmetric volatility impulse response dealing with non-normality 163–4 function (AVIRF) 311–12, 317–21, estimating model error 164 322, 323 estimating sampling error 167 asymmetrical information 283 estimating VaR 167–8

365 366 INDEX basic multivariate normal (BMVN) Canadian government yield curve method continued 97–102, 103 incorporation of hedging constraints capital asset pricing model (CAPM) 165–6 278–9, 280–4 incorporation of sampling error 162 conditional see conditional CAPM Bayesian model averaging 164 ADC model Bekaert, G. 329 decision rule 282–3 BEKK model 330 capital charge for operational risk asymmetric VaR-BEKK model 1–21 309–11, 312–17, 322 capital investment projects 278–302 Berkowitz, J. 216 Carr, P. 357 Bermudian options 210 Ceci, V. 48 beta central limit theorem (CLT) 285–301 volatility and debt 118–23 and the first-order autoregressive volatility transmission in Europe process 297–301 342–4, 345, 351 and the NPV probability distribution binomial distribution 4 285–97; simulation models and negative 4–5 statistical tests 288–9; simulation Black, F. 109, 110, 117, 194 results 289–93; theoretical results Black–Scholes pricing model 285–7 109, 198, 201, 208, 353, 356 certainty equivalent approach 282–3 195–7 CEV-ARCH models 90–1 blank sheet syndrome 205 Chambers, J.M. 148 block maxima method 7 Chapelle, A. 8 Blume, L. 48 Chatfield, C. 216 Blume, M. 280 Chen, L. 70 Bock, B. 242 Chen, R.-R. 125 Bodnar, O. 243, 258 chi squared test 5 Bohn, J. 109 Christie, A.A. 329 Bollerslev, T. 54, 115, 246, 266, 311, Christoffersen, P. 214, 215, 216 330, 335 collection threshold 2, 8–16, 17 Bollinger bands 87, 99, 100, 101–2, 103 impact on capital charge for bond portfolios 69–85 operational risk 9–11; empirical bonds analysis 11–16, 17, 18, 19 inflation-linked 172–3; optimal selection 8–9 portfolios 176–82 Collin-Dufresne, P.P. 108, 124 inflation-linked products and comparative Bayesian analysis 221–2, hedging 182–9 223 zero-coupon see zero-coupon bonds conditional CAPM ADC model Booth, G. 305 329–51 Borgonovo, E. 50, 51 asymmetries analysis 342–5 bounds for credit spreads 125–6 model estimates 335–41 Braun, P.A. 329 volatility spillovers 345–8, 349–50 British stock market 331–51 conditional correlations 210 Britten-Jones, M. 258 conditional volatility 86–7, 88–92 burn analysis 160–1 Conover, W. 163 Conrad, J. 328 constant correlation coefficient model CAC40 index 331–51 266, 330 calibration, model 200 Cont, R. 360 call options 74–5, 158 convexity, generalized 74, 76–7 Campbell, J.Y. 87, 108, 111 copulas 163–4 Campbell, S.D. 215 correlated frailty intensity-based Campolongo, F. 49, 59 models 143–6 INDEX 367 correlation breakdowns 226–40 de Haan, L. 7 correlation jumps and volatility De Jong, F. 103 behaviour 228–36 debt, volatility and 118–23 data and descriptive statistics 226–8 debt financing 285 impact on portfolio optimization debt pricing see credit risk valuation 237, 238, 239 decrease in slope of yield curve correlation matrix 161, 162–3 (flattening) 79–81 correlations default events correlations 134, 136, between default events see default 138–9, 150–1 events correlations and default probabilities in empirical study of time-varying intensity-based models 139–41 return correlations and the efficient large time horizons 139, 152–4 set of portfolios 265–77 default probabilities model risk and 210 intensity-based models 137; and costless contracting 283–4 default events correlations Courtadon, G. 210 139–41 covariance Merton-style models 133, 134 asymmetric 328–9, 348, 349–50, 351 default risk 108 conditional 342–7 deflation protection 178–81 covariance structure of asset returns Delbaen, F. 22, 24–5, 27, 28 and optimal portfolio weights Delianedis, G. 108 243–6 dependence levels 132–55 monitoring changes in covariance comparison between dependence matrix see sequential control indicators 139–43 procedures extensions of basic intensity-based Cox model 136–7 model 143–50 Crama, Y. 8 intensity-based models 136–9 Cramer–von Mises test 6 Merton-style models 133–6 crash-phobia 196 derivatives 26, 34, 35, 159 credit risk valuation 107–31 evolution of pricing models 194–5 general model 110–14; basic setting model risk and 191–212 110–12; and model selection and its impact on Merton’s pricing 112–14 hedging 353–64 simulation study 118–26; credit role of models for 197–9 spread 123–6, 127; volatility and see also under individual types of debt 118–23 stochastic volatility model 114–17 Derman, E. 192, 354 credit spreads 123–6, 127 deterministic () models crises 304 354 Crnkovic, C. 216 Di Graziano, G. 357, 358, 360 Crocket, J. 280 Diebold, F.X. 103, 115, 216, 246 Crosier, R.B. 249 differential importance measure 49, cross-section approach to VaR 50–1, 65–6 backtesting 217–24 trading strategies and 58–65 applications 219–24 DIPO 8 CUSUM control charts 248–50 discount bonds price 70–2 projected pursuit CUSUM 249–50, discount rates 286–7, 288, 290–3, 252–3 293–4 vector valued CUSUM 249 diversification-based risk measure 22–46 daily level simulation 165–6 economic motivation 29–30 Danilov, D. 103 implementation 33–7 data verification 208 numerical example 31–3 Day, J. 92 pricing portfolio insurance 37–43 368 INDEX diversification-based risk measure exotic derivatives 209–10 continued expiry value 167 properties of the measure 27–8, extended Kalman filter (EKF) 87, 94, 44–5 95 dollar-denominated risk 26–7 algorithm 96 insurance and 42–3 application to Fong and Vasicek double exponential distribution 288, model 96–7 291–3, 294 simulation of interest-rate term Dow Jones Industrial Average Index structure 99–103 time-varying return correlations and extreme value theory 7–8, 12–16, 217 efficient set of portfolios 269–76 algorithm for finding the threshold trading strategies through sensitivity 8, 12, 18–19 analysis 56–66 Drachman, J. 216 failures analysis 222–4 Drudi, F. 48 falsifiability 281 Dupire, B. 354 Fama, E.F. 108, 280, 282 duration 69–70, 84 Fernández, A. 304 generalized 72–4, 75 Figlewski, S. 192 proposed solution for limitations of financial crises 304 75–83 financial derivatives see derivatives Durbin-Watson statistic 229, 230, 239 financial distress, probability of 283–4 dynamic conditional correlation (DCC) financial services 57, 63, 64 models 266, 268–76 financing of a firm 285 firm preferences 35–7 Ebens, H. 115, 246 first-order autoregressive process Eber, J.M. 22, 24–5, 27, 28 286–7, 288, 289–93, 297–301 Eberlain, E. 109 Fisher equation 171 economic motivation 29–30 Flannery, M.J. 285 efficient market hypothesis 282 flattening of yield curve 79–81 efficient set of portfolios 265–77 Follmer, H. 23, 28 El Karoui, N. 357 Fong, H.G. 87 elasticity 48–9, 51, 53, 65 Fong and Vasicek model 87, 93–4 Elton, E.J. 108 application of extended Kalman filter Embrechts, P. 4, 7 to 96–7; discretization 96–7; energy sector 57, 63, 64, 65 linearization 97 Engle, R.F. 53–4, 86, 266, 268, 330, 342 calibration 98 Eom, J.H. 109, 128 data 97–8 equilibrium models of interest rate simulation of interest rate term term structure 92, 93 structure 99–103 equity 121–2 Fornari, F. 87, 90–1 equity financing 285 forward contracts 26, 34 Eraker, B. 354 forward-looking models 200 Ericsson, J. 127 Frachot, A. 3, 8, 9 Euro area 226–36 frailty models 136–7 Europe, volatility transmission in see also intensity-based models 327–52 French, K.R. 108, 280 European call options 172 French stock market 331–51 debt pricing 113–14, 116–17 frequency distribution 4–5, 17 EWMA control chart Frey, R. 48 comparison of multivariate and frictionless economy 282 simultaneous 254–8 Friedman, M. 280 multivariate 250–1, 254–8, 259 Friend, I. 280 simultaneous 253, 254–8, 259 Frisen, M. 242, 258 exchange traded contracts 158 FTSE100 index 331–51 INDEX 369 futures contracts 26, 34, 35 model risk and 202–3 super-hedging strategies 203 Galluccio, S. 357, 358, 360 hedging error 355, 356–63 Gallus, C. 203 analytical expression of total hedging Gamma 358–9, 362–3 error 357–9 GARCH models 48 numerical results 359–63 conditional volatility 89, 90, 91 Helwege, J. 109, 128 importance of portfolio weights in Hendry, O.L. 328 GARCH volatility estimation Hentschel, L. 342 models 53–6, 66 Hertz, D.B. 278 multivariate see multivariate Heston, S. 354, 356 GARCH models heteroskedasticity 339 Gatfaoui, H. 109, 110, 111, 126 Hicks, D. 158, 160 Gemmill, G. 124 Hillier, F. 278, 285–6 Generale, A. 48 Hirsa, A. 210 Generalized Pareto Distribution hit function, tests based on 214–15 (GPD) 7 Hoeffding, W. 286 generalized scenarios 27 Hofmann, N. 112 geometric Brownian motion 171–2 Hon, M.T. 304, 323 Georges, P. 3 Hotelling, H. 248 German stock market 331–51 Houston, J.F. 285 Geske, R. 108 Huang, J.-Z. 109, 125, 128 Gibbons, M.R. 258 Hübner, G. 8 Gibson, R. 192 Hull, J. 109, 354 Glaser, M. 304 hurdle rates 281 global minimum variance portfolio (GMVP) 242, 243–6, 247 Iachine, I.A. 143 global risk models 222 IBEX35 index 305–8, 312–23 Glosten, L.R. 330, 344 idiosyncratic risk 107–31 Goetzmann, W.N. 128 illiquidity 35–7 Goldstein, R.S. 108, 124 Iman, R. 163 goodness-of-fit tests 5–6, 9–10 implied volatility 109, 195–7, 354 Gourieroux, C. 48 increase in slope of yield curve Goyal, A. 108–9 (steepening) 81–2, 83 Green, T.C. 192 independence property 215 Greenspan, A. 195 inflation index Gruber, M.J. 108 modeling the evolution of 171–3 Gultekin, M.N. 328 optimal portfolios 178, 179 Gumbel, E.J. 7 inflation-linked products 170–90 Gunther, T.A. 216 hedging with 182–9; investment in bond and stock 186–7; Hagan, P. 360 investment in bond, stock and Hamao, Y. 305 inflation 184–6; numerical harmonized consumer price index examples 188–9 (HCPI) 171 optimal portfolios with 173–82 Healy, J.D. 248 information asymmetries 283 Heath, D. 22, 24–5, 27, 28 information and communication hedging technologies (ICT) 57, 63, 64 constraints 165–6 insurance of derivatives and model selection contracts 159 353–64 portfolio see portfolio insurance with inflation-linked products intensity-based models 132–55 182–9 comparisons between dependence managing interest rate risk 74–5 indicators 139–43 370 INDEX intensity-based models continued kurtosis 270, 271, 274, 306, 307 default events correlations 138–9 α extensions 143–50; -stable lambda 118–23 distributions 146–50; multi-factor Lange, R. 92 model 143–6 large capitalization stocks 327–52 loss distribution 137–8, 142–3 Laughhunn, D.J. 283 interest rate risk see two-factor model Laurent, J.P. 48 for interest rates Le Cam, Y. 360 interest rate term structure forecasting Ledoit, O. 163, 241, 258 87, 92–103 Lee, D. 304 data and calibration of Fong and left tail risk 88–9 Vasicek model 97–8 Leland, H.E. 122 empirical results 99–102, 103 leptokurtic distributions 5, 6 methodology 94–7 Lesniewski, A. 360 models 92–4 Lettau, M. 111 simulation 98–9 leverage effect hypothesis 328–9 inventory of models in use 204–5 Levy, H. 280–1 Ito, H. 304 Lhabitant, F.S. 192 Li, C. 103 Jagannathan, R. 281, 330 likelihood weighting 164 Japan 226–36 Lin, W.L. 317 Jarque-Bera test 270, 271, 274, 306, 307 Lintner, J. 278 Jarrow, R. 23, 189 liquidity 127 Jeanblanc, M. 357 illiquidity 35–7 Jensen, M.C. 283 liquidity premium 127 Jewson, S. 157, 162, 163, 164, 167 Ljung–Box test 307 Jobson, J.D. 258, 265 Lo, A.W. 327 Johannes, M. 354 local volatility (LV) models 354 Jones, S. 157 location parameter 147 Jostova, G. 108 long time horizons 139, 152–4 jump-diffusion (JD) models 354 Longin, F. 305 Kallsen, J. 109 Lopez, J.A. 217 loss distributions Kalman filter 94 α extended see extended Kalman -stable intensity-based model filter 149–50 Kani, I. 354 intensity-based models 137–8, Kaul, G. 328 142–3 Kealhofer, S. 127 measuring operational risk 3–8; Kearney, C. 310 empirical analysis 12–16; Kocagil, A.E. 109 frequency distribution 4–5, 17; Kolmogorov–Smirnov test 6, 9, 10, 11 modeling extreme losses 7–8; Koopman, S.J. 108 severity distribution 5–7, 12, 13, Korkie, B.M. 258, 265 16, 17 Korn, R. 170, 172, 173, 174, 176–7, Merton-style models 134–5, 142–3 183–5 multi-factor intensity-based model Koutmos, G. 305 144 Kraft, H. 170, 173 loss functions, backtesting VaR models Kristen, J. 109 based on 217 Kroner, K.F. 266, 328, 330, 342, 344 Lucas, A. 108 Kruse, S. 170, 172 Luenberger, D.G. 34 Kumar, A. 128 Kumar, D. 360 Mackinlay, A.C. 327 Kupiec, P. 215, 220 Madan, D.B. 210, 357 Kurbat, M. 127 Mahmoud, M.A. 258 INDEX 371

Majnoni, G. 48 illustration 195–7 Malkiel, B.G. 108, 111 model-building process and model Mallows, C.L. 148 risk creation 199–201 Mandal, K. 103 rules for managing 203–10; Manganelli, S. 48, 54, 57, 66, 67 correlations 210; define a Mann, C. 108 model-testing framework 205–6; manufacturing 57, 63, 64, 65 define what should be a good market frictions 33, 35–7 model 204; exotic indices 331–51 209–10; keeping track of models in market risk 69, 83 use 204–5; marking to market market value 167–8 206–7; regular revision of models marking to market 206–7 206; simplicity 207–8; stress marking to model 206–7 testing of models 209; use a Markowitz, H. 194, 241, 243, 265 model for its purpose 209; Martens, M. 305 verification of data 208 Martin, J.S. 108 model selection 199–200 Masulis, R.W. 305 and its impact on hedging maximum likelihood estimation (MLE) derivatives 353–64 techniques 3–4 model-testing framework 205–6 MC1 control charts 248, 252, 254–8 model usage 200–1, 204 McNeal, A.J. 48 model validation team 205 mean absolute error 234–5, 236 Modigliani–Miller (MM) paradigm mean excess function (MEF) plot 7–8, 281, 282 12, 14 monotonicity 28 mean square error (MSE) 12, 15 Monte Carlo simulation 87 mean-variance optimization models comparison of multivariate and 265–6, 276 simultaneous control charts Meckling, W.H. 283 253–5 Meier, I. 281 forecasting interest rate term Mele, A. 87, 90–1 structure 98–102; Bollinger bands Meneu, V. 311, 317 99; empirical results 99–102, 103 Merrill Lynch 208 Moreno, M. 70, 74 Merton, R.C. 23, 109, 110, 124, 192, 194 Mossin, J. 278 credit pricing model and stochastic motivation, economic 29–30 volatility 112–14, 127–8 Moudoulaud, O. 8, 9 Merton-style credit risk models Moustakides, G.V. 249 132–6, 142–3, 150 Michaud, R.O. 265–6 moving average specification 266 MIDCAC index 331–51 Muirhead, R.J. 259 Miller, M.H. 280 multifactor models Mills, T.C. 88 intensity-based 143–6 minimal equivalent martingale interest rate term structure 93 measure 113–14, 126 multiple VaR levels 216–17 misspecification indicators 344–5 multivariate CUSUM (MCUSUM) model-building process 199–201 control charts 249, 252, 254–8 model calibration 200 multivariate EWMA (MEWMA) control model selection/creation 199–200 charts 250–1, 254–8, 259 model usage 200–1 multivariate GARCH models model error 164 time-varying return correlations and model-implied calibration 354–5 the efficient set of portfolios model misspecification 359, 360–1 265–77 model risk 191–212, 355 volatility spillovers in Europe 330–1 case study 201–3 volatility transmission between USA examples and consequences 193 and Spain 303–26 372 INDEX multivariate normal distribution see European call options 113–14, basic multivariate normal (BMVN) 116–17, 172 method exotic 209–10 multivariate statistical surveillance out-of-the-money options 26, 34, 35 246–51 orthogonalization 309 comparison of multivariate and ORX 8 statistical control charts 253–8 out-of-control states 247, 255–8 multivariate t-distribution 244–5 out of sample model efficiency 234–5, Myers, S.C. 283 236 out-of-the-money options 26, 34, 35 NatWest 206 over the counter (OTC) contracts 158 negative binomial distribution 4–5 negative returns 273 parallel change in yield curve 77–9 Nelken, J. 109 parameters misspecification 359–60, Nelson, D.B. 86–7, 90 361–3 news impact surfaces 342–4 Parner, E. 143, 144 Ng, V.K. 266, 305, 328, 330, 342, 344 partial derivatives (PDs) 48–9, 50–1, Ngai, H.-M. 248, 249, 250 52–3, 65 no-arbitrage models 92, 93 Patton, A.J. 310 no default risk 281 peak over threshold (POT) method 7 non-normality 163–4 Peccati, L. 50, 51 non-synchronous trading problem Peña, J.I. 304 304–5 Penzer, J. 162 normal distribution 288, 289, 290, 294 Perez, J.V. 304 NPV probability distribution 278–302 perfect economy 280–2 and the central limit theorem Peters, J.P. 8 285–97; simulation models and Philipov, A. 108 statistical tests 288–9; simulation Philips, T. 242 results 289–93; theoretical results Philips and Perron test 307 285–7 Phoa, W. 128 systematic risk and the perfect Pickands, J. 7 economy 280–2 Pignatiello, J.J. 248 total risk and the real economy Pistre, N. 192 282–5 Platen, E. 112 Poisson distribution 4 one-factor models of interest rate term Pollak, M. 249 structure 92–3 Polson, M. 354 operational risk 1–21 Poon, S.H. 305 collection threshold 8–11; empirical Popper, K. 281 analysis of impact 11–16, 17, 18, portfolio holdings-based risk measure 19 see diversification-based risk measuring 3–8 measure optimal weight changes 57, 58–63, portfolio insurance 23, 30 65–6, 67 pricing 37–43; insurance and optimization, portfolio see portfolio dollar-denominated risk 42–3; optimization insurance with rebalancing option pricing models 199 39–42; insurance without Black–Scholes model see rebalancing 38–9 Black–Scholes option pricing portfolio optimization model covariance structure of asset returns model risk 201–3 and optimal portfolio weights option pricing theory 112–14, 116–17 243–6 options 158 impact of correlation jumps 237, call options 74–5, 158 238, 239 INDEX 373

with inflation-linked products Roncalli, T. 3, 8, 9 173–82 root mean square error (RMSE) 100–2, time-varying return correlations and 103 the efficient set of portfolios Ross, S.A. 258, 328 265–77 Rubinstein, M. 196 portfolio rebalancing see rebalancing Runger, G.C. 248 portfolio weights see weights, Runkel, D.E. 330 portfolio positive homogeneity 28 S&P500 index 305–8, 312–23 Poterba, J.M. 281 SABR model 360 Poteshman, A.M. 304 preferences Saltelli, A. 48, 49, 59 firms’ 35–7 sampling error 162, 167 model user’s 204 Santa-Clara, P.P. 108–9 price of risk 335–7, 351 Sarnat, M. 280–1 price risk 77 savage score correlation coefficients pricing error 202 (SSCC) 49, 59–65 probability density function 216–17 Savickas, R. 119 projected pursuit CUSUM (PPCUSUM) Scaillet, O. 48 control charts 249–50, 252–3 scale parameter 146–7 proportional weight changes 53, 55, scenario tests 164 58–63, 65–6 Schied, A. 23, 88 purpose, model’s 209 Schipper, S. 242, 247 put options 158 Schmid, W. 242, 244, 247, 258 Scholes, M. 109, 110, 117, 194, 280 QQ plots 12, 13 see also Black–Scholes option pricing quantile regression 217 model quasi-debt leverage ratio 124–5 Schönbucher, P.J. 139–40 Schoutens, W. 359 Ramchand, L. 305 Schwebach, R.G. 108 ratchet options 210 Schweizer, M. 112 real economy 282–5 Schwert, G.W. 246, 254, 329 real option theory 279 SDAX index 331–51 rebalancing 23, 27, 30, 31–2, 33–4 second-order autoregressive process portfolio insurance with 39–42 289, 293 record keeping 204–5 sensitivity analysis (SA) reinvestment risk 77 background 50–1 relative weight changes 51–3 impact of collection threshold on relevance 28 capital charge for operational risk Renault, O. 127, 143 16, 17, 18, 19 Revised Framework of the portfolio volatility 47–68; effect of International Convergence of relative weight changes 51–3; Capital Measurement and Capital importance of portfolio weights in Standards (Basel II) 1–2, 8 GARCH volatility estimation revision of models 206 models 53–6; trading strategies risk measurement see through SA 56–65 diversification-based risk September 11 2001 terrorist attacks measurement 272, 273, 303 riskfree capital monotonicity 28 impact on volatility transmission RiskMetrics 226–8 patterns between USA and Spain Robbins, H. 286 303–26 robust conditional moment test 344–7 sequential control procedures 241–64 Rockafellar, R.T. 23 comparison of multivariate and Roll, R. 281 simultaneous control charts rolling estimator 267–76 253–8; 374 INDEX

behavior in the out-of-control state statistical surveillance 242 255–8; comparison of multivariate and sequential control procedures, behavior simultaneous 253–8 continued multivariate 246–51 structure of Monte Carlo study simultaneous 251–3 253–5 steepening in yield curve 81–2, 83 covariance structure of asset returns Stein, E.M. 354, 356 and optimal portfolio weights Stein, J.C. 354, 356 243–6 Stein, R.M. 109 multivariate statistical surveillance Steinand, D. 242 246–51 stochastic volatility 48, 86–106, 354 simultaneous statistical surveillance and conditional volatility 86–7, 251–3 88–92 Servigny, A. de 143 idiosyncratic risk, systematic risk severity distribution 5–7, 12, 13, and 107–31; simulation study 16, 17 118–26; stochastic volatility and Shanken, J. 258 Merton’s pricing 112–14; Sharma, J. 328 stochastic volatility model 114–17 Sharpe, W.F. 107, 194, 278 and interest rate term structure Shaw, S. 284 forecasting 87, 92–103 Shephard, N. 54 stocks short selling constraints 267 hedging with inflation-linked shortest path 28 products 182–9 shorthand, models as 197–8 large and small capitalization stocks Shreve, S. 357 in Europe 327–52 shrinkage 162–3 optimal portfolio and shrinking method 249 inflation-linked bonds 181–2 Simon, C.P. 48 Strauss, J. 304, 323 Simons, E. 359 stress testing for models 209 simplicity 207–8 Stuck, B.W. 148 simultaneous MEWMA control statistic Stulz, R.M. 283, 284, 285 253, 254–8, 259 subadditivity 28 simultaneous statistical surveillance Summers, L.H. 281 251–3 Sunderman, M.A. 108 super-hedging strategies 203 comparison of multivariate and Susmel, R. 305 statistical control charts 253–8 swaps 26, 34, 158 single contracts 166–7 systematic risk 279 skewness 270, 271, 274 idiosyncratic risk, stochastic skewness parameter 146–7 volatility and 107–31 SMALL CAP index 331–51 and the perfect economy 280–2 small capitalization stocks 327–52 smile 109, 196, 354 T2 control charts 248, 252, 254–8 Solnik, B. 305 Taksler, G.B. 108 Spahr, R.W. 108 Talay, D. 192 Spain–USA volatility transmission Tay, A.S. 216 patterns 303–26 Taylor, S.J. 89 spreadsheet syndrome 205 telecommunication 57, 63, 64 Sprecher, C.R. 283 term structure of interest rates stability, index of 146–7 forecasting see interest rate term standard portfolio analysis of risk structure forecasting (SPAN) risk management system terminal portfolio values 24–5 25, 27 terrorism see September 11 2001 standardized approach (SA) 2 terrorist attacks state–space representation 95–7 Thakor, A.V. 284 INDEX 375

Theodossiou, P.T. 242 Vanna 359, 362–3 three-stage least-squares (3SLS) method variance 98 large and small capitalization stocks time-varying return correlations 342–4, 348, 351 265–77 mean–variance optimization models Tistaert, J. 359 265–6, 276 Torra, S. 304 Vasicek, O.A. 87 Torró, H. 311, 317 Vecchiato, W. 48 total risk 279 VECH model 330 and the real economy 282–5 vector valued CUSUM 249 trading hours, non-synchronous Vega 359 304–5 Venkataraman, S. 285 trading/reallocation strategies 56–66 verification of data 208 transaction costs 35–7 volatility transparent economy 282–3 asymmetric 328–9, 348, 349–50, 351 Trautmann, S. 170, 173, 174, 176–7 conditional 86–7, 88–92 truncation 9–11 correlation jumps and 228–36, two-factor model for interest rates 237–9; portfolio optimization 237, 69–85 238, 239 basic model 70–2 GARCH models compared with generalized duration and convexity rolling estimates for time-varying 72–4 return correlations 271–2 hedging ratios 74–5 implied 109, 195–7, 354 proposed solution for limitations of sensitivity analysis of portfolio the conventional duration 75–83 volatility 47–68 Tzotchev, D. 242 spillovers between large and small firms 345–8, 349–50 unconditional correlations 268–76 stochastic see stochastic volatility unconditional coverage property 215 transmission between large and uniform probability distribution 288, small firms in Europe 327–52 290–1, 294 transmission patterns between USA uniform weight changes 52–3, 55, and Spain 303–26 58–63, 65–6 volatility feedback hypothesis 328–9, United States (USA) 328 337, 348 correlation jumps with Euro area and volatility impulse response function Japan 226–36 (VIRF) 311 volatility transmission patterns volatility smile 109, 196, 354 between Spain and 303–26 volatility surface 196–7 Volga 359, 362–3 value-at-risk (VaR) 22, 48, 213–25 asymmetric VaR-BEKK model 309–11, 312–17, 322 Wagle, B. 278, 286 cross-section approach 217–24; Wald, A. 248 comparative Bayesian analysis of Wang, S. 163 performance 221–2, 223; failures weather derivative portfolios 156–69 analysis 222–24; intuitive accurate estimation of correlation example 219–21 matrix 162–3 review of existing methods for consistency between valuation of backtesting 214–17; tests based single contracts and portfolios on hit function 214–15; tests 166–7 based on multiple VaR levels or dealing with non-normality 163–4 entire probability density function defining risk for 159–60 216–17 estimating model error 164 weather derivatives portfolio risk estimating sampling error 167 167–8 estimating VaR 167–8 376 INDEX weather derivative portfolios continued Wu, G. 329 incorporation of hedging constraints 165–6 incorporation of sampling error 162 Xu, Y. 108, 111 methods of estimating risk in 160–2 nature of weather derivatives 157–9 Yashchin, E. 242 Weber, M. 304 Yashin, A.I. 143 weights, portfolio yield curve 69–70, 83–4 covariance structure of asset returns forecasting stochastic volatility and and optimal portfolio weights 86–106 243–6 shifts in 77–83 importance in GARCH volatility yield curve options 209–10 estimation models 53–6, 66 yields 76–83 relative weight changes 51–3 Yildirim, Y. 189 White, A. 109, 354 Yong, S. 304, 323 Wolf, M. 163, 241, 258 Wongswan, J. 305 Woodall, W.H. 258 zero-coupon bonds 72–4 Woodward, D. 360 inflation-linked 173, 177–81 Wooldridge, J.M. 311, 335, 342, 344, Zhang, J. 248, 249, 250 345 Ziemba, W.T. 23