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ENCYCLOPEDIA OF QUANTITATIVE FINANCE Volume 3 K-Q Editor-in-Chief RAMA CONT CNRS, Paris, France and Columbia University, New York, USA WILEY Contents VOLUME 1 Basket Options 164 Bates Model 166 ABS Indices 1 Behavioral Portfolio Selection 168 Accumulated Claims 4 Bermudan Options 175 Actuarial Premium Principles 7 Bermudan Swaptions and Callable Adverse Selection 13 Libor Exotics 177 Affine Models 16 Bernoulli, Jacob 181 Algorithmic Trading 20 Bid-Ask Spreads 184 Alternating Direction Implicit (ADI) Binomial Tree 190 Method 30 Black, Fischer 194 Altiplano Option 37 Black-Litterman Approach 196 Ambiguity 39 Black-Scholes Formula 199 American Options 44 Bond 207 Arbitrage Bounds 53 Bond Options 212 Arbitrage: Historical Perspectives 61 Bubbles and Crashes 216 Arbitrage Pricing Theory 71 Butterfly 230 Arbitrage Strategy 74 Arrow, Kenneth 76 Call Auction Markets 233 Arrow-Debreu Prices 82 Call Options . 236 Asian Options 87 Call Spread 239 Asset-Liability Management 91 Capital Asset Pricing Model 241 Atlas Option 107 Caps and Floors 250 Autocall 108 Catastrophe Bonds 253 Automated Trading 111 CDO Square 255 Autoregressive Moving Average CDO Tranches: Impact on Economic (ARMA) Processes 114 Capital 257 Average Strike Options 120 Change of Numeraire 264 Cliquet Options 268 Bachelier, Louis (1870-1946) 123 CMS Spread Products 269 Backtesting 127 Collateralized Debt Obligation (CDO) Backward Stochastic Differential Options . 273 Equations 134 Collateralized Debt Obligations Backward Stochastic Differential (CDO) 278 Equations: Commodities and Numeraire 284 Numerical Methods 145 Commodity Forward Curve Modeling 291 Barndorff-Nielsen and Shephard Commodity Price Models 298 (BNS) Models 152 Commodity Risk • 303 Barrier Options 155 Commodity Trading ,' 308 Base Correlation 158 Compensators 314 Basket Default Swaps 161 Complete Markets . 317 xii Contents Conjugate Gradient Methods 324 VOLUME 2 Constant Elasticity of Variance (CEV) Diffusion Model 328 Early Exercise Options: Upper Constant Maturity Credit Default Bounds 507 Swap 334 Econometrics of Diffusion Models 512 Constant Maturity Swap 338 Econometrics of Option Pricing 518 Constant Proportion Portfolio Economic Capital 528 Insurance 344 Economic Capital Allocation 531 Convertible Bonds 347 Econophysics 535 Convex Duality 350 Efficient Market Hypothesis 538 Convex Risk Measures 355 Efficient Markets Theory: Historical Convexity Adjustments 363 Perspectives 542 Copulas: Estimation 368 Electricity Forward Contracts 546 Copulas in Econometrics 375 Electricity Markets 549 Copulas in Insurance 379 Emissions Trading 555 Correlation Risk 382 Employee Stock Options 561 Correlation Swap 386 Entropy-based Estimation 567 Corridor Options 387 Equity-Credit Problem 571 Corridor Variance Swap 392 Equity Default Swaps 575 Counterparty Credit Risk 393 Equity Swaps 577 Cox-Ingersoll-Ross (CIR) Model 401 Equivalence of Probability Measures 580 Cramer-Lundberg Estimates 404 Equivalent Martingale Measures 583 Cramer's Theorem 407 Esscher Transform 589 Crank-Nicolson Scheme 410 Eurodollar Futures and Options 592 Credibility Theory 414 Exchange Options 594 Credit Default Swap (CDS) Indices 420 Exchange-traded Funds (ETFs) 611 Credit Default Swap Index Options 422 Execution Costs 612 Credit Default Swaps 424 Exercise Boundary Optimization Credit Default Swaption 431 Methods 617 Credit Migration Models 434 Expectations Hypothesis 621 Credit Portfolio Insurance 441 Expected Shortfall 630 Credit Portfolio Simulation 447 Expected Utility Maximization 634 Credit Rating 450 Expected Utility Maximization: Credit Risk 456 Duality Methods 638 CreditRisk+ 459 Exponential LeVy Models 646 Credit Scoring 462 Exposure to Default and Loss Given Currency Forward Contracts 467 Default 651 Extreme Value Theory 657 Default Barrier Models 475 Default Time Copulas 479 Factor Models 669 Delta Hedging 482 Filtering • 674 Discretely Monitored Options 484 Filtrations 683 Dispersion Trading 486 Finite Difference Methods for Barrier Diversification 487 Options 687 Dividend Modeling 489 Finite Difference Methods for Early Doob-Meyer Decomposition 493 Exercise Options 695 Drawdown Minimization 495 Finite Element Methods 704 Duffle-Singleton Model 499 Fisher, Irving 711 Dupire Equation 501 Fixed Mix Strategy 714 Duration Models 504 Foreign Exchange Basket Options 717 Contents xiii Foreign Exchange Markets 722 Implied Volatility: Market Models 916 Foreign Exchange Options 727 Implied Volatility in Stochastic Foreign Exchange Options: Delta- Volatility Models 920 and At-the-money Conventions 731 Implied Volatility Surface 926 Foreign Exchange Smile Implied Volatility: Volvol Expansion 931 Interpolation 742 Infinite Divisibility 935 Foreign Exchange Smiles 745 Inflation Derivatives 938 Foreign Exchange Symmetries 752 Insurance Derivatives 948 Forward and Swap Measures 760 Insurance Risk Models 952 Forward-Backward Stochastic Integral Equation Methods for Free Differential Equations (SDEs) 763 Boundaries 956 Forward-starting CDO Tranche 770 Intensity-based Credit Risk Models 963 Forwards and Futures 773 Intensity Gamma Model 966 Fourier Methods in Options Pricing 778 Internal-ratings-based Approach 968 Fourier Transform 782 Intraday Price Efficiency 973 Fractional Brownian Motion 787 Inventory Effects 976 Free Lunch 790 Ito, Kiyosi (1915-2008) 979 Fundamental Theorem of Asset Ito's Formula 981 Pricing 792 Jarrow-Lando-Turnbull Model 985 Gamma Hedging 803 Jump-diffusion Models 987 Gamma Swap em Jump Processes 990 GARCH Models 809 Gaussian Copula Model 820 VOLUME 3 Gaussian Interest-Rate Models 828 Generalized Hyperbolic Models 833 Kelly Problem 995 Generalized Method of Moments Kolmogorov, Andrei Nikolaevich 998 (GMM) 836 Kou Model 999 Gerber-Shiu Function 841 Kyle Model 1005 Glosten-Milgrom Models 842 Good-deal Bounds 846 Large Deviations 1009 Large Pool Approximations 1017 Lattice Methods for Path-dependent Hazard Rate 853 Options 1022 Heath-Jarrow-Morton Approach 856 Leveraged Super-senior Tranche 1027 Heavy Tails 860 LIBOR Market Model 1031 Heavy Tails in Insurance 873 LIBOR Market Models: Simulation 1036 Hedge Funds 875 LIBOR Rate 1041 Hedging 881 Life Insurance 1042 884 Hedging of Interest Rate Derivatives Limit Order Markets 1057 889 Heston Model Liquidity 1062 898 High-frequency Data Liquidity Premium 1066 Himalayan Option 904 Loan Valuation 1071 Hull-White Stochastic Volatility, Local Correlation Model 1075 Model 905 Local Times 1078 Local Volatility Model 1080 Implied Volatility: Large Strike Lognormal Mixture Diffusion Model 1086 Asymptotics 909 Long Range Dependence 1088 Implied Volatility: Long Maturity Long-Term Capital Management 1091 Behavior 913 Lookback Options 1096 xiv Contents LeVy Copulas 1104 Oil Market 1315 LeVy Processes 1108 Operational Risk 1319 Optimization Methods 1322 Managed CDO 1113 Option Pricing: General Principles 1327 Mandelbrot, Benoit 1115 Option Pricing Theory: Historical Margrabe Formula 1118 Perspectives 1331 Market Microstructure Effects 1120 Options: Basic Definitions 1341 Market Risk 1123 Order Flow 1344 Market Transparency 1131 Order Types 1349 Markov Functional Models 1138 Ornstein-Uhlenbeck Processes 1352 Markov Processes 1142 Markovian Term Structure Models 1159 Parisian Option 1355 Markowitz, Harry 1164 Partial Differential Equations 1357 Martingale Representation Partial Integro-differential Equations Theorem 1166 (PIDEs) 1363 Martingales 1171 Passport Options 1368 Mean-Variance Hedging 1177 Performance Measures 1372 Measurements Errors 1181 Phase-type Distribution 1375 Merton Problem 1184 Point Processes 1376 Merton, Robert C. 1188 Poisson Process 1380 Method of Lines 1191 Portfolio Credit Risk: Statistical Minimal Entropy Martingale Methods 1384 Measure 1195 Predictability of Asset Prices 1387 Minimal Martingale Measure 1200 Price Impact 1402 Mixed Data Sampling 1204 Pricing Formulae for Foreign Mixture of Distribution Hypothesis 1207 Exchange Options 1408 Model Calibration 1210 Pricing Kernels 1418 Model Validation 1219 Probability of Informed Trading 1428 Modeling Correlation of Structured Pseudorandom Number Generators 1431 Instruments in a Portfolio Put-Call Parity 1437 Setting 1220 Quadratic Gaussian Models 1441 Models 1226 Modern Portfolio Theory 1232 Quadrature Methods 1444 Modigliani, Franco 1239 Quantization Methods 1451 Modigliani-Miller Theorem 1241 Quanto Options 1455 Moment Explosions 1247 Quasi-Monte Carlo Methods 1460 Monotone Schemes 1253 Monte Carlo Greeks 1263 VOLUME 4 Monte Carlo Simulation 1266 Monte Carlo Simulation for Stochastic Random Factor Loading Model Differential Equations 1271 (for Portfolio Credit) . 1473 Multifractals 1278 Random Matrix Theory 1476 Multigrid Methods 1283 Rare-event Simulation 1481 Multiname Reduced Form Models 1288 Rating Transition Matrices 1484 Multivariate Distributions 1296 Real Options 1488 Municipal Bonds 1300 Realized Volatility and Multipower Mutual Funds 1304 Variation 1494 Realized Volatility Options 15,60 Nested Simulation 1307 Recovery Rate 1505 Normal Inverse Gaussian Model 1311 Recovery Swap 1507 Contents xv Recursive Preferences 1509 Stochastic Differential Equations Reduced Form Credit Risk Models 1517 with Jumps: Simulation 1693 Regime-switching Models 1522 Stochastic Differential Equations: Regulatory Capital 1525 Scenario Simulation 1697 Reinsurance 1539 Stochastic Discount Factors 1706 Risk-adjusted Return on Capital Stochastic Exponential 1714 (RAROC) 1544 Stochastic Integrals 1717 Risk Aversion 1546 Stochastic Mesh Method 1726 Risk Exposures 1554 Stochastic Taylor Expansions 1731 Risk Management: Historical Stochastic
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