Synthetic CDOs, mounfield

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Synthetic CDOs, mounfield

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SYNT HE T IC CDOs Modelling, Valuation and Risk Management Credit derivatives have enjoyed explosive growth in the last decade One of the most important assets in this industry is synthetic Collateralised Debt Obligations (synthetic CDOs) This book describes the state-of-the-art in quantitative and computational modelling of these instruments Starting with a brief overview of the structured finance landscape, the book introduces the basic modelling concepts necessary to model and value simple vanilla credit derivatives Building on this the book then describes in detail the modelling, valuation and risk management of synthetic CDOs A clear and detailed picture of the behaviour of these complex instruments is built up The final chapters introduce more advanced topics such as portfolio management of synthetic CDOs and hedging techniques, often not covered in other texts Mathematics, Finance and Risk Editorial Board Mark Broadie, Graduate School of Business, Columbia University Sam Howison, Mathematical Institute, University of Oxford Neil Johnson, Centre of Computational Finance, University of Oxford George Papanicolaou, Department of Mathematics, Stanford University S Y NT H E TI C C DOs Modelling, Valuation and Risk Management CRAIG MOUNFIELD CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521897884 © C C Mounfield 2009 This publication is in copyright Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published in print format 2008 ISBN-13 978-0-511-46551-2 eBook (NetLibrary) ISBN-13 978-0-521-89788-4 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate Dedicated to my parents, my wife and my daughter Contents Preface Acknowledgements A primer on collateralised debt obligations 1.1 Introduction 1.2 Securitisation and tranching 1.3 Credit derivative products 1.4 Chapter review Modelling of obligor default 2.1 Introduction 2.2 Modelling single-name default as a Poisson process 2.3 Modelling default correlation – fundamental concepts 2.4 Introducing default dependence via copulas 2.5 Rating transition methods for modelling obligor default 2.6 Chapter review Valuation of credit default swaps 3.1 Introduction 3.2 Overview of vanilla credit default swaps 3.3 Valuation of vanilla CDSs 3.4 Calibration of the survival curve to market observed data 3.5 Risk sensitivities of vanilla CDSs 3.6 Chapter review Credit indices 4.1 Introduction 4.2 Description of the credit indices 4.3 Index trading mechanics 4.4 Valuation of credit indices 4.5 Time series analysis of credit indices vii page xi xvi 1 24 25 25 26 31 33 36 43 45 45 46 51 58 62 65 66 66 67 69 72 73 viii Contents 4.6 Tranched credit index exposures 4.7 Chapter review Valuation of default baskets 5.1 Introduction 5.2 Brief overview of default baskets 5.3 General valuation principles for default baskets 5.4 Analytic valuation of default baskets in simple limiting cases 5.5 Monte Carlo valuation of default baskets 5.6 Phenomenology of default baskets 5.7 Semi-analytic valuation of default baskets 5.8 Chapter review Valuation of synthetic CDOs 6.1 Introduction 6.2 Synthetic CDO cashflow mechanics 6.3 Basic principles of synthetic CDO pricing 6.4 Valuation in the standard market model using Monte Carlo simulation 6.5 Valuation in the standard market model using semi-analytic techniques 6.6 Structural models 6.7 Chapter review Phenomenology of the standard market model 7.1 Introduction 7.2 Baseline case analysed 7.3 Tranche loss statistics 7.4 Analysis of the portfolio loss distribution 7.5 Correlation and maturity sensitivity of the tranche par spread 7.6 Default baskets revisited 7.7 Chapter review Risk quantification of synthetic CDOs 8.1 Introduction 8.2 Synthetic CDO risk factors 8.3 Baseline case analysed 8.4 Quantifying credit spread sensitivities – CS01 8.5 Quantifying correlation sensitivities – correlation vega 8.6 Quantifying default risk sensitivities – value-on-default (VoD) 8.7 Tranche time decay 8.8 Credit spread value-at-risk (CVaR) 78 80 81 81 82 84 86 89 93 105 108 110 110 111 114 118 121 133 135 137 137 137 138 142 149 158 158 160 160 160 162 163 172 174 177 181 Contents 10 11 12 13 14 8.9 Default value-at-risk (DVaR) 8.10 Chapter review Implied and base correlations 9.1 Introduction 9.2 Market quoting conventions 9.3 The correlation smile and implied correlation 9.4 The market solution – base correlations 9.5 Chapter review Extensions of the standard market model 10.1 Introduction 10.2 Extending the standard market model 10.3 Dynamic portfolio loss models 10.4 Chapter review Exotic CDOs 11.1 Introduction 11.2 Synthetic CDO2 and CDOn 11.3 Cashflow CDOs 11.4 Asset backed CDS (ABCDS) 11.5 ABX indices and tranched ABX (TABX) exposures 11.6 Chapter review Correlation trading of synthetic CDO tranches 12.1 Introduction 12.2 An overview of correlation trading 12.3 Delta hedging of synthetic CDO tranches 12.4 Analysis of common correlation trading strategies 12.5 Credit market dislocations 12.6 Chapter review Risk management of a portfolio of synthetic CDOs 13.1 Introduction 13.2 Set-up of the problem 13.3 Portfolio risk measures 13.4 Description of the sample portfolio 13.5 Basic analysis of the sample portfolio 13.6 Adding new trades to the portfolio 13.7 Origination of synthetic CDOs 13.8 Chapter review Hedging simulation of structured credit products 14.1 Introduction 14.2 What is hedging simulation? 14.3 Hedging of structured credit products ix 184 189 190 190 191 192 197 203 204 204 205 221 222 224 224 225 229 241 243 247 249 249 250 258 264 270 276 277 277 278 285 289 292 302 305 308 309 309 310 313 Simulated annealing 355 Table B.1 Results of the different algorithms for calculating the global minima of the test functions Random sampling Case A Case B Case C Gradient following Simulated annealing x f (x) x f (x) x f (x) 2.33 4.70 2.35 −0.79 −0.95 −0.98 8.62 11.00 8.64 −0.42 −0.90 −0.92 2.33 4.70 8.64 −0.79 −0.95 −0.92 0.8 Case A - lambda = 0.1, omega = Case B - lambda = 0.01, omega = 0.6 Case C - lambda = 0.01, omega = 0.4 0.2 0 10 −0.2 −0.4 −0.6 −0.8 −1 Figure B.1 The three different parameterisations of the function f (x) = e−λx sin ωx computed analytically for this one-dimensional example Sampling x at random 10 000 times also does a good job of identifying the true minima However, a gradient based approach where the algorithm simply moves downhill from its initial position can easily return a local minimum The performance of the simulated annealing algorithm is a little more subtle Consider the three cases A, B and C with parameters as shown in Figure B.1 Table B.1 shows the results of applying the three different minimisation strategies In all cases the initial starting value for the algorithm was x0 = (deliberately chosen so as to be close to a local minimum, but far away from the true global minimum) In all cases random sampling does a very good job of finding the global minimum (because the problem is one-dimensional) The gradient follower, however, finds only a local minimum 356 Appendix B Table B.2 Impact of annealing schedule on the performance of the algorithm for case C (near degenerate global minimum) Simulated annealing Annealing schedule x f (x) 0.909 0.990 0.999 8.64 5.50 2.35 −0.92 −0.95 −0.98 because the starting value of x0 = is poor In cases A and B simulated annealing does a very good job of finding the global minimum However, in case C it only finds a local minimum This is because case C has almost degenerate global minimum since λ → The random sampling method is unaffected by this since the function parameters have no influence on where the algorithm samples from But the simulated annealing algorithm is not able to explore adequately the macro shape of the function This is because the annealing schedule is too rapid Table B.2 reports the performance of the simulated annealing algorithm as the annealing schedule is slowed down Because the system spends more time at higher temperatures there is now a greater chance for the algorithm to jump out of the local minimum that it finds itself in As the annealing schedule is reduced the algorithm eventually finds the true global minimum This example highlights an important practical point when employing simulated annealing as a stochastic search technique Specifically, a poor choice of parameters can lead to poor performance Although simulated annealing is an intuitive and powerful technique, it requires the analyst to have a good understanding of the problem they are trying to solve In the above example it was easy to see when the algorithm performed poorly A real problem, however, may not be so simple to interpret It is advised before using simulated annealing that a good understanding of the actual problem is obtained Simulated annealing is a beautiful and powerful method, but it requires some expertise to get the best out of it References H Albrecher, S A Ladoucette and W Schoutens, A Generic One-factor Levy Model for Pricing Synthetic CDOs, www.defaultrisk.com, May 2006 C Alexander, Market Models: A Guide to Financial Data Analysis, Wiley, 2001 C Alexander and S Narayanan, Option pricing with normal mixture returns, ISMA Centre Discussion Papers In Finance, December 2001 K A Allman, Modeling Structured Finance Cashflows with Microsoft Excel, Wiley, 2007 L Andersen, Portfolio Losses in Factor Models: Term 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Wilmott, Paul Wilmott on Quantitative Finance, Volumes and 2, Wiley, 2000 G Xu, Extending Gaussian Copula with Jumps to Match Correlation Smile, www.defaultrisk.com, December 2006 J Yang, T Hurd and X Zhang, Saddlepoint Approximation Method for Pricing CDO’s, www.defaultrisk.com, November 2005 F Yu, Correlated defaults in intensity based models, 17 (2), 155–173, 2007 Index ABCDS, see asset-backed CDSs ABSCDO 14, 226, 231, 246, 272, 273, 279 ABS securities 226, 273 ABX index 12, 67, 241, 243 accrued coupon payment 71, 92 accrued fee payment 48 all upfront 16, 20, 254, 257 alpha-stable model 219 annuity payments 51 antithetic variables 58 Archimedean copula 213 asset asset backed commercial paper 273 asset backed securitisation (ABS) 14 asset backed security,see ABS securities asset correlation matrix 134 asset-backed CDSs 241 assets 20 attachment points 111, 114, 139 auto-correlation 183 auto-correlation function 77 automobile loans base correlation 126, 157, 197, 198, 205, 219, 246, 256, 275, 283, 292, 314 base correlation curve 193, 199 base correlation surface 202, 219 Bayes rule 32 Bernoulli random variable 215 bespoke pool 256 bespoke synthetic CDO 18, 19 bespoke synthetic tranches 278 bespoke tranche 19, 79, 196, 200, 202, 203, 205, 246 beta distribution 141, 161, 342 bids wanted in competition 254 bi-lateral swap contract 111 binomial distribution 131 bisection method 197 Black option valuation model 221 Black–Cox models 133 Black–Karasinski 344 Black–Scholes 77, 192 bootstrapped 60, 97, 219 bootstrapping, see bootstrapped bottom-up 284 bucketed CS01 64 buyer of protection 251 calculation agent 46, 48 call-spread option 198 call-spread payoff 115 capital buffer 21, 22 capital model 21 capital structure 4, 12, 13, 111, 139, 238, 252 caplets 312 cashflow CDO 13, 120, 229, 239, 241, 278 cashflow waterfall 12, 13, 232, 246, 278 cash settlement 47 Cauchy distribution 210 CBO 231, 278 CDO Evaluator 141 CDO squared 225, 279, 284 CDS 31, 46 CDS index 292, 335 CDS par spread 56 CDS spreads 39 CDX crossover index 68 CDX high yield index 68, 80 CDX HiVol index 68 CDX index 12, 18, 67 CDX investment grade index 68, 80 central difference approximation 167 central differences, see central difference approximation central limit theorem 33 Chapman–Kolmogorov equation 38 characteristic function 128 Cholesky decomposition 35, 36, 89, 90, 91, 119, 134, 184, 227, 234, 317 CIR 344 cliff risk 14, 226 clip sizes 69 CLO 231, 278 clustering of defaults 112 co-dependence 31 364 Index collateralised bond obligation (CBO) 14, 229 collateralised loan obligation (CLO) 14, 229 collateralised swap obligation 16 combinatorial complexity 303 commercial paper 22, 23, 274 complete market 311 compound correlation 192 concentration risk 287 conditional default probability 107, 126, 129 conditional independence 106 conditional pseudo hazard rates 214 conditional survival probability 106 connectivity matrix 227, 290, 291, 303, 306, 338 connectivity vector 303 constant maturity CDS (CMCDS) constant maturity swap contagion models 334 contagion of defaults 315 contingent payment 47, 51, 54, 191 convexity 64, 98, 99, 100, 103, 164, 166, 169, 174, 258 convolution 106, 122, 207, 208 copula 33 copula models 205 correlated default times 89, 90, 96, 118, 139 correlated variance gamma process 220 correlation 12, 19, 62 correlation crisis 74, 75, 213, 216, 270, 272, 322 correlation matrix 32, 35, 172, 217, 283, 315, 317, 341 correlation sensitivity 256, 257 correlation skew 202, 217, 283 correlation smile 193, 195 correlation trading 174, 250 correlation vega 172, 286 cost function 212 counterparty credit exposure 341 counterparty credit exposure measurement 337 counterparty exposure 337 counterparty risk 62, 86 coverage tests 239 Cox process 29 credit card receivables credit crunch 20, 74, 75, 272, 275 credit default swaptions 8, 76, 279 credit derivative 46, 272, 278 credit derivative index credit event notice 48 credit exposure simulation 338 credit index 72, 255 credit indices, see credit index credit limits 337 CreditMetrics 105 credit portfolio modelling 105 credit rating 37, 292 credit risk 46 credit risk factors 162 credit spikes 338, 348 credit spread sensitivity 63 credit spread value-at-risk 181 credit triangle 57, 63 365 critical default time 83, 92, 99, 100 cross-subordination 228 CS01 63, 293 cumulative normal distribution function 90, 106 curve flatteners 8, 47 curve steepeners 8, 47 DBRS 291 dealer poll 47 default barrier level 105 default baskets 10, 82, 93, 117, 133, 158, 166, 250, 252, 262, 279, 320 default contagion 335, 336 default correlation 31, 35, 89, 97, 156, 172, 192, 195, 215 default correlation matrix 89, 119, 234 default event 83 default indicator 334 default intensity 28 default probability 27 default protection 49 default risk 65 default times 35, 49, 57, 91, 93, 115, 138, 171 default time simulations 92 default VaR 184, 289 default/jump times 27 delinquencies 272 delta 168, 253, 258, 261, 264 delta exchange 18, 255 delta hedge 258, 264, 314 delta hedged 255, 256, 257, 263, 264, 266, 268, 269, 270, 271, 275 delta hedged equity tranche 269 delta hedging 83, 254, 257, 259, 260, 263 delta neutral 258 delta sensitivities 98 deltas 103, 347 detachment points 111 digital CDS disordered systems 282, 304 DLLs 240 double t model 207 drift 134, 318, 327 duration 47 dV01 243, 261 dynamic factor models 220 dynamically hedge 312 economic capital 339, 343 eigenvalues 91 eigenvectors 91 embedding problem 41 equity curve flattener 276 equity (residual) piece 230 equity tranche 4, 111 Excel add-ins 240 excess kurtosis 76 expected shortfall 333, 339, 343 factor models 105, 121, 197, 214, 341 fee leg 47 fee payments, see fee leg 366 Index filtered probability space 334 filtration 38, 334 finite-state Markov chain 334 first-to-default basket 10, 158, 316 Fitch 5, 291 Fitch Vector model 133 Ford 271 foreclosures 272 forward starting CDOs 20, 221 forward starting CDS Fourier method 132 Fourier transform 129 FtDs 259, 314 FTSE 100 index 73 functional copula 214 fundamental theorem of asset pricing 311 future rates 85 gains process 335 gamma 264, 286 gamma diffusion process 218 gamma function 342 gamma processes 218 gamma risk 285 gap risk 285 Gauss–Hermite 125, 130, 321 Gaussian copula 35, 36, 130, 139, 202, 206, 217, 222, 233, 315, 336 generalised hyperbolic distributions 207 generalised Poisson process 220 General Motors 271 generator matrix 40, 41, 339 genetic algorithms 303, 308 geometric Brownian motion 134, 183, 317, 321, 331, 344 global minima 305 Greeks 251 grid computing 347 gross exposure 341 hazard rate 27, 29, 36, 259, 318 Heaviside step function, see Heaviside unit step function Heaviside unit step function 99 hedge ratio 261, 262, 265, 266, 269, 317, 319, 336 hedging and replication 313 hedging error 333 hedging simulations 86, 312, 319, 320 hedging strategies 315 hedging strategy 261, 311, 332 historical data 313, 338, 343 HJM/BGM 222 hockey stick 193 home equity loans homogeneous Poisson distribution 53 Hull–White model 30, 344 idiosyncratic component 105, 122 idiosyncratic defaults 228, 252, 267, 271, 272, 275, 287, 314 implied correlations 126, 192, 195, 197, 256, 270, 275, 320, 322 implied volatility 192 incomplete market theory 336 indenture 232 index par spread 72 index roll 69 index roll-time 69 index spread 127 index trading 71 index trading strategies 71 index tranches 17, 79, 192, 292 indicator function 85, 115 inhomogeneous Poisson process 28 inner or baby CDOs 225 intensity gamma 219 interest collections account 232, 236, 239 interest coverage test 231, 232, 240 interest rate swap internal rate of return 20, 232 International Money Market (IMM) dates 50 inverse gamma distribution 206 investor redemptions 272 Ito’s lemma 321, 344 iTraxx Asia Ex Japan 68 iTraxx Australia 68 iTraxx capital structure 115, 138 iTraxx crossover index 68 iTraxx HiVol index 68 iTraxx index 12, 18, 67, 80, 184, 270, 280 iTraxx Japan index 68 iTraxx main index 68 JLT methodology 37, 41, 42 joint default behaviour 33 joint survival probability 86 junior liabilities 230 KK method 43 kurtosis 210 large homogeneous portfolio 130, 132 LCDS 48 LCDX index 12 leverage 226, 246, 254 leveraged corporate loans 232 leveraged exposure 48, 253 leveraged position 78 Levy base correlation 218 Levy process 218 LHP approximation, see large homogeneous portfolio LHP model, see large homogeneous portfolio liability 4, 20 linear correlation 31, 32 linear correlation matrix 32 linear interpolation 200 linear models 96, 104 liquidity 2, 274 Index local minima 305 long correlation 117, 253, 256 look-through 284 loss distribution, see portfolio loss distribution macro hedges 252 managed, see managed tranches managed tranches 314 mapping vector 290, 291 marginal CS01 166, 169, 170, 293, 297 marginal default probability 106, 174 marginal distributions 32 marginal gammas 167 marginal probability density 34 marginal survival curve 119 marginal VoD 174, 175, 297 market efficiency 311 market risk factors 161 market standard model 233 MarkIt 11, 67, 192 Markov, see Markov chain Markov chain 39, 40, 339, 341 Markov chain model 336 Markovian 28 mark-to-market 13, 22, 47, 272 Marshall–Olkin copula 213 master CDO 225 master tranche 285 matrix exponential 41 matrix inversion 260 matrix logarithm 41 maximum likelihood estimation 346 MBS bonds 234 MBSs 273 mean-reversion 30, 344, 345 Mersenne twister 90 Merton model 105, 122, 133, 231 mezzanine micro hedges 252 micro-hedging 23 mixture of Gaussian distributions 206 model choice 312 model risk 162, 311 modified Bessel function of the third kind 208 moment generating function 208 monetize the P/L 264 money market rates 85 Monte Carlo estimators 92, 98, 117, 169, 347 Monte Carlo simulation 23, 30, 57, 86, 90, 93, 103, 118, 132, 134, 138, 164, 236, 243, 279, 280, 318, 347 Monte Carlo simulation error 94 Moodys 5, 68, 291 mortgages MtM accounting 161 multi-factor models 220 multiple CS01 170 multivariate distribution 34 multivariate Gaussian copula 35 multivariate joint probability density 34 367 multivariate normal 129 multivariate student t copula 36 multivariate student t distribution 36 net exposure 341 Newton–Raphson 90 no-arbitrage pricing theory 311, 315 non-recombining binomial tree 127 normal copula 89, 92, 313, 334 normal distribution 33, 75, 77, 88, 210, 212 normal gamma process 220 normal Gaussian copula 89 normal inverse Gaussian distribution 207 normally distributed 106, 107, 122, 125, 206 normal proxy, see normal proxy model normal proxy method 132 normal proxy model 129, 151, 321, 347 Nth-to-default basket 85 object oriented 132, 228, 240 objective function 303 objective (historical) measure 346 obligor concentration risk 285, 287 obligor default 26 offers wanted in competition 255 off-the-run 69, 203, 256 one-factor model 205 one-sided differences 64 on-the-run 68, 203, 256, 292 options on synthetic CDOs 221 options on tranches 20 over-collateralisation 231, 239, 279 over-collateralisation test 231, 232 overlap matrix 287 over the counter 48 parallel processing 305, 347 par CDS spreads 106, 280 pari passu 11, 47 participation rate 10 path dependence 300 path dependent 135 pay-as-you-go 241 physically settled physical settlement 47 Poisson distributed 220 Poisson process 27, 28 pool loss 139 pool notional 114 pool occupancy fractions 291, 307 portfolio loss distribution 103, 118, 126, 130, 132, 139, 142, 149, 154, 156, 157, 168, 171, 174, 192, 195, 212, 213, 216, 222, 251, 275, 347 portfolio loss models 220, 222 portfolio manager 280 positive carry 255, 265, 268 positive convexity 262, 264, 266, 268, 269, 275 positive gamma 270, 275 positive semi-definite 91 potential future exposure 132, 337, 348 power-law decay 78 368 pre-payments 15, 23, 234 price discovery 59, 202, 231 principal collection account 232, 236 principal protected structures 19 principal redemptions 4, 235 private equity probability generating function 216 probability mass leakage 127 probability measure 334 protection purchaser 7, 47, 111 protection seller 7, 47, 111 quadratic model 104 quenched disorder 282 ramp up 16, 229, 251 ramp-up period random factor loading model 217 random number generators 89, 96, 339 random number seed 305, 323 range-accrual note 347 rating agency rating migration 41, 339 ratings arbitrage 13 rating transition matrix 41, 42, 338 real-world rating transition matrices 41 recovery amount 42 recovery rate 7, 47, 280, 342 recovery rate lock recursive method 123, 126, 130, 132, 142, 151, 185, 212, 229, 347 reduced-form 37 reduced-form model 40 reference obligation 47 regulatory capital regulatory capital relief 13 reinvestment period 232 replicating portfolio 310, 311 residual hedging error 336 residual/first-loss piece risk management 22, 278, 292 risk manager 285 risk-minimizing hedging strategies 336 risk-neutral measure 29, 311, 334, 346 risk-neutral pricing theory 333 risk-neutral rating transition matrices 41 risk-neutral transition matrix 38, 39 risk-neutral transition probabilities 42 risky bond 29 risky duration 54, 63, 73 risky dV01 53 running coupon basis 16 running spread 113, 118, 191, 257, 264, 332 running VoD 176, 184, 285, 289, 297 sample standard deviation 95 sampling with replacement 183 second-to-default basket 85 securitisation 2, 6, 21, 274 Index securitise 273 seed risk 96 seller of protection 251 semi-analytic 105, 108, 120, 123, 130, 132, 144, 151, 169, 174, 195, 206, 229, 285, 296, 347, 348 senior liabilities 230 senior tranches series 68 short correlation 117, 174, 253, 256, 270 simulated annealing 213, 257, 303, 308, 346 simulated default times 99 simulation seed 96 single-tranche CDO 12, 15, 79, 128, 250 single-name CDSs 250 SIV-lite 21 SIVs 274 skewness 76, 210 Sklar’s theorem 34 slave CDO 225 slave tranches 285 special purpose vehicle 3, 231 spline 201 spot delta neutral 265 spread convexity 262, 263 spread curve rotation 64 spread inversion 345 spread leverage 253 spread volatility 65 SPV Standard & Poors 5, 68, 140, 271, 291 standard indices 280 standardised credit indices 250 standardised index 78 standardised index tranches 203 standardised indices 17, 121, 241 standardised tranched exposures 245 standardised tranches 79, 205, 241 standard market model 118, 195, 202, 205, 217, 221, 315, 336 standard model, see standard market model state dependent 215 state independent 215 state variable 334 static 12, 16, 229, 254 static hedging 331 STCDOs 253, 255, 256, 264, 270, 271, 278 stochastic correlation 215 stochastic differential equation 30, 339 stochastic spread dynamics 334 structural models 105, 133, 217, 220 structured investment vehicle (SIV) 20 student t copula 206 subordination 5, 111, 114, 115, 155, 157, 158, 174, 177, 189, 198, 226, 228, 229, 231, 239, 329 sub-prime 272 sub-prime mortgages super senior tranche 114 survival curve 56, 60, 64, 90, 97, 243 survival probability 27, 28, 29, 30, 42, 53, 57, 60, 220, 235 Index swap rates 85 swaptions 312 synthetic CDOs 6, 12, 15, 19, 48, 83, 91, 103, 105, 107, 111, 121, 134, 158, 160, 191, 194, 221, 225, 229, 250, 258, 275, 279, 313 synthetic securitisation 15 systemic component 105, 122 systemic default 267 systemic risk 228, 252, 275, 287, 314 TABX index 67 TABX tranches 241, 243, 279 t-copula 36 temperature 305 the basis 71 the roll 68 theta 177, 312 traded deltas 255 tranche 4, 280 tranche default probability 139 tranched exposures tranche duration 265 tranche expected loss 140 tranchelets 20, 201 tranche leverage 255 tranche loss-given-default 140 tranche MtM 118 369 tranche par spread 117 tranche subordination 111, 128 tranche technology 78 tranche upfront payment 118 tranching 2, 6, 21 transition matrix 37, 40, 41, 335, 341 uniform distribution 57 universe of obligors 280 upfront payment 20, 70, 113, 138, 176, 191, 244, 257, 264, 265, 292, 332 value-on-default 65, 127, 285, 289 VaR 182, 184, 301, 333, 339, 343 variance gamma process 334 variance reduction techniques 58, 82 VIX index 75 volatility 8, 20, 30, 68, 134, 263, 275, 315, 318, 323, 329, 346 warehouse waterfall structure 120, 230 weighted average spread 306 weighting factor 105 wrong-way exposure 344 zero-coupon bond 20, 42, 258 zero-coupon equity tranche 20 ... of default baskets 5.8 Chapter review Valuation of synthetic CDOs 6.1 Introduction 6.2 Synthetic CDO cashflow mechanics 6.3 Basic principles of synthetic CDO pricing 6.4 Valuation in the standard... about the modelling, valuation and risk management of synthetic collateralised debt obligations (or synthetic CDOs or simply CDOs for short) Synthetic CDOs are an example of a structured credit... topic, synthetic CDOs, and introduce some of the basic modelling tools necessary to describe them Chapters 4–10 analyse the mathematical and computational modelling techniques applied to synthetic

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