3GBINDEX 11/18/2013 16:4:36 Page 315 Index Albanese, C., 285 about, 251–252 Altman E., 61 Basel I, 23–24, 252 Andersen, L., 134 Basel I, reason for, 23 Anderson, M., 65 Basel II, 23, 153, 252 Anderson Darling test, 51 Basel II, credit value at risk ARCH model, 50, 161, 177 (CVaR) approach, 252–258 Artificial intelligence and financial Basel II, default probability- modeling, 287–299 default correlation relationship, Bayesian probabilities, 295–297 259–260 chaos theory, 291–295 Basel II, reason for, 23 chaos theory and finance, Basel II, required capital (RC) for 293–295 credit risk, 258–259 fuzzy logic, 290 Basel III, 23, 153, 252, 262 genetic algorithms, 290–291 Basel III, credit value at risk genetic fuzzy neural algorithms, (CVaR) approach, 262 291 Basel III, reason for, 23 neural networks, 287–289 and double default treatment, Artificial neural network (ANN), 269–274 288 double-default approach, Asset modeling, 174–176 270–274 Asset value, 159 substitution approach, Asymptotic single risk factor (ASRF) 269–270 approach, and correlation, Basel Committee for Banking 274 Supervision, 16 Attractor, 292 Baxter, N., 134 Autocorrelation (AC), 50 Bayes, Thomas, 295 Bayesian methods, 297, 299 Backhaus, J., 134 Bayesian probabilities, 295–297 Backpropagation, 288, 298 Bayesian statistics, 299 Backwardation techniques, 289 Bayesian theorem, 295–296 Bahar, R., 74 Bellaj, T., 285 Basel, derivative multiplier, 268–269 Binomial approach, 213 Basel accords. See also Correlation Binomial correlation approach, and Basel II and III 212 315 Correlation Risk Modeling and Management: An Applied Guide Including the Basel III Correlation Framework—with Interactive Correlation Models in Excel/VBA, First Edition. Gunter Meissner. © 2014 John Wiley & Sons Singapore Pte. Ltd. Published 2014 by John Wiley & Sons Singapore Pte. Ltd. 3GBINDEX 11/18/2013 16:4:37 Page 316 316 INDEX Binomial correlation measure Capital asset pricing model. See about, 72–73 Black-Scholes-Merton (BSM) binomial correlation measure option pricing model application, 73–74 Capital charge, 17, 273–274 vs. Pearson correlation model, 90 Capponi, A., 215 Binomial correlation measure Carr, P., 148, 159 application, 73–74 Cash CDOs, 103 Bivariate Gaussian copula, 75 n1, CDO’s (collateralized debt 132 obligations). See Collateralized Bivariate normal distribution, 80, debt obligations (CDOs) 270 CDS (credit default swap). See Black, F., 108, 176 Credit default swap (CDS) Black-Scholes-Merton (BSM) 1973 Chang, E., 148, 159 option pricing model, 9, 58, Chaos theory, 291–295, 299 106, 167 and finance, 293–294 Black-Scholes-Merton (BSM) option and finance application, 294–295 pricing model, 6 Chaotic system criteria, 291 Bollerslev, T., 160–161, 176 Cherubini, U., 65 Bond correlation Chi-squared test, 51 and default probability Cholesky decomposition, 81, 91–93, correlations, 53–54 116, 132 distribution, 54 Circularity, 89, 151 Bounded Jacobi process, 165–167 Clark, P., 148 Brace, A., 176 Clustering of volatility, 161 Brigo, D., 72, 215, 221, 225 Collateralized debt obligations Briys, E., 109 (CDO’s) Brooks, B., 61 about, 101–102 Brown, R., 163 advantages, 102–103 Brun, Marie-France, 169 basics, 101–105 Bubbles, 18–19 binomial correlation valuation, 73 Buraschi, A., 169, 171–172, 176 CDO complexity, 114 Buraschi, Porchia, and Trojani correlation, 222 model (2010), 168–169, global financial crisis, 18–19 171–172, 176 market price risk, 183 Burtchell, X., 65 model limitations in valuation, Buying correlation, 11 115 problems with Gaussian copula Calibration valuation, 113–116 financial models, 59 recovery rate, 113 Gaussian Copula limitations, 87 types of, 103–105, 115 Call options, 237 valuing, 105–113 buying and selling, 13 Commodity market, 181 3GBINDEX 11/18/2013 16:4:37 Page 317 Index 317 Commodity risk, 14 definition, 182 Computational finance, 284 financial practice examples, Concentration ratio, 33 184–187 Concentration risk, definition, 30 financial practices, 182–184 Conditional correlation, 162 and Gora in investments, Conditional defaults, 121 187–189 Conditional VaR risk, 24 measures of, 198–199 Conditionally independent default of risk/return ratio, 187 (CID) Cora financial practice examples application of, 149 in market risk management, contagion correlation models, 90 189–197 correlation approach, 134 option Cora and Gora, 185–187 correlation modeling, 122 option Vanna, 184–185 OFGC model, 120, 138 Cora in market risk management Constant asset correlation, vs. about, 189–195 stochastic asset correlation, 163 Gap-Cora, 196–197 Cont, R., 148 Correlated default distribution, Contagion correlation, 134 111 Contagion correlation models, Correlated default risk, 33 88–91, 148–150 Correlated default time Contagion default modeling, derivation of, 124 150–153 for multiple assets, 81–82 Copula applications, 85 using survival principles, 82–84 Copula correlation model, 18, 60 Correlated market risk, 33 Copula correlations Correlating Brownian motions, 90. about, 74–75 See also Geometric Brownian advantages and limitations, 90–91 motion (GBM) copula applications, 85 Correlation correlated default time for definition, 34–35 multiple assets, 81–82 definition by usage, 36–37 correlated default time using Correlation, basics, properties and survival principles, 82–84 terminology Gaussian copula, 76–81 about, 1–2 Gaussian copula limitations, correlation risk, 2–5 85–88 correlation risk as part of finance Copula functions, 75 risk, 24–33 Copula model, 27, 58 finance usage, 6–24 Copulas, limitations of, for finance, Correlation, empirical properties 90–91 bond correlations and default Cora probability correlations, 53–54 of a CDO, 229–230 equity correlation and for CDSs, 223–225 autocorrelation, 50–51 3GBINDEX 11/18/2013 16:4:37 Page 318 318 INDEX Correlation, empirical properties Correlation modeling future, (Continued) numerical finance, 283–287 equity correlation distribution, Correlation models, 34 51–52 Correlation risk equity correlation volatility as about, 2–5 indicator, 52–53 in Basel framework, 278 in expansion through recession in a collateralized debt obligation periods, 43–46 (CDO), 227 mean reversion and, 46–49 and concentration risk, 30–33 summary, 54–55 Cora for different tranches, 230 Correlation and Basel II and III Cora parameter, 182 Basel accords, about, 251–252 and credit risk, 25–27 Basel accords and double default hedging correlation risk, 238 treatment, 269–274 and market risk, 24 Basel II and III credit value at as part of finance risk, 24–33 risk (CVaR) approach, quantification of, 195 252–258 and systemic risk, 27–30 Basel II required capital (RC) for types of, 34–35 credit risk, 258–260 wrong-way risk (WWR), 222 credit value adjustment (CVA) Correlation risk as part of finance with wrong-way risk (WWR), risk, 24–33 264–269 correlation risk and concentration credit value adjustment (CVA) risk, 30–33 without wrong-way risk correlation risk and credit risk, (WWR), 261–264 25–27 debt value adjustment (DVA), correlation risk and market risk, 274–276 24 funding value adjustment (FVA), correlation risk and systemic risk, 276–278 27–30 wrong-way risk quantification, terminology, 33–34 268–269 summary, 34–35 summary, 278–279 Correlation risk in CDO Correlation coefficient, 33–34 Cora of a CDO, 229–230 Correlation concept Gora of a CDO, 230–231 about, 128–129 types of risk, 227–228 loss distribution of, 129–130 Correlation risk parameters Cora tranche spread-correlation and Gora, 182–184 relationship, 130–131 Correlation smile, 87, 136 Correlation desks, 8, 33 Correlation swap, 11–13, 244–245 Correlation hedge, 189 payoff of, 12 Correlation matrix, 75 n1 Correlation swap hedge, 246 Correlation modeling, 144 Correlation trading, 8, 33 3GBINDEX 11/18/2013 16:4:37 Page 319 Index 319 Correlation via stochastic time indexes, 104 change, 148–150 market price risk, 183 Correlation via transition rate payoff tree, 206–208, 216–217 volatilities, 146–147 payoff tree and CDS spread Correlation volatility, 45, 53 payment tree, 219–220 Correlation-dependent option, payoff tree and CDS spread tree, 239–244 210–211 Counter-party default risk, 211 premium tree, 206 Counter-party risk, 102 vs. put option, 247 Counting process, 152 spread, 205 Covariance, 36 spread impact testing, 211–213 Covered put buying, 236 spread payment tree, 217–219 Cox, J., 108, 184 spread tree, 207–210 Cox-Ingersoll-Ross (CIR) process, in synthetic CDO, 103 70, 173, 221 Credit exposure, 266, 268 Credit collection risk Credit products, 183 definition, 202 Credit risk positive vs. negative, 204 collateralized debt obligation Credit correlation, 34 (CDO), 101–102, 227 Credit correlation risk, 231 and correlation risk, 24 Credit correlation risk quantification credit exposure, 266 about, 201–203 credit value at risk (CVaR) in a CDS, 203–205 calculation, 252, 263–264 correlation risk in CDO, 227–231 types of, 201 pricing CDSs including credit Credit triangle, 112 correlations, 215–227 Credit value adjustment (CVA) pricing CDSs with entity- types of correlations, 23, 251 counterparty credit correlation, without wrong-way risk (WWR), 205–215 261–264 summary, 231–232 with wrong-way risk (WWR), Credit counterparty risk, 251 264–269 Credit default swap (CDS). See also Credit value at risk (CVaR) Pricing CDSs Basel accord, 251–253, 271 bond risk, 208–210 copula model, 58 counterparty risk with correlated default risk, 33 correlation-dependent option, default probability PD(T), 257 239–244 definition, 252 in a credit correlation risk valuation, 253 quantification, 203–205 Crossover method, 290 defined, 13 n3 Cumulative default probability, definition,