Index [] · Index σ-algebra,729 Markov property,164 complementrule,731 absenceofarbitrage,25,559...

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Index σ-algebra, 729 Markov property, 164 complement rule, 731 absence of arbitrage, 25, 559 abstract Bayes formula, 517 accreting swap, 597 adapted process, 149 adjusted close price, 202, 678 admissible portfolio strategy, 181 affine model, 553 affine PDE, 305, 553, 1022 American binary option finite expiration, 508 perpetual, 508 forward contract, 510 option call, 479, 489 dividend, 503, 506 finite expiration, 493 perpetual, 479 put, 479 amortizing swap, 597 annuity measure, 632 annuity numéraire, 596, 631, 647 approximation gamma, 573 lognormal, 438 arbitrage, 21 absence of, 25 continuous time, 181 discrete time, 56 opportunity, 22 price, 14, 39, 68, 78, 254 triangular, 21 arithmetic average, 427 Asian option, 427, 429 basket, 444 call, 427 dividends, 457 hedging, 457 asset pricing first theorem, 27 continuous time, 183, 601 discrete time, 67 second theorem, 33 continuous time, 186 discrete time, 68 at the money, 57, 268 attainable, 31, 37, 77, 186 Bachelier model, 191, 230, 236, 269 backward induction, 86, 89 backward stochastic differential equation, 274 Bank for International Settlements, 9 Barone-Adesi & Whaley approximation, 500, 502, 981 barrier forward contract, 396 down-and-in long, 397, 939 down-and-out long, 397, 940 up-and-in long, 397, 935 up-and-out long, 397, 937 barrier level, 371 barrier option, 58, 367, 371 down-and-in call, 372, 385 put, 372, 387 1087

Transcript of Index [] · Index σ-algebra,729 Markov property,164 complementrule,731 absenceofarbitrage,25,559...

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Index

σ-algebra, 729Markov property, 164complement rule, 731

absence of arbitrage, 25, 559abstract Bayes formula, 517accreting swap, 597adapted process, 149adjusted close price, 202, 678admissible portfolio strategy, 181affine model, 553affine PDE, 305, 553, 1022Americanbinary optionfinite expiration, 508perpetual, 508

forward contract, 510optioncall, 479, 489dividend, 503, 506finite expiration, 493perpetual, 479put, 479

amortizing swap, 597annuitymeasure, 632

annuity numéraire, 596, 631, 647approximationgamma, 573lognormal, 438

arbitrage, 21absence of, 25continuous time, 181discrete time, 56opportunity, 22price, 14, 39, 68, 78, 254triangular, 21

arithmetic average, 427Asian option, 427, 429basket, 444call, 427dividends, 457hedging, 457

asset pricingfirst theorem, 27continuous time, 183, 601discrete time, 67

second theorem, 33continuous time, 186discrete time, 68

at the money, 57, 268attainable, 31, 37, 77, 186

Bachelier model, 191, 230, 236, 269backward induction, 86, 89backward stochastic differential equation,

274Bank for International Settlements, 9Barone-Adesi & Whaley approximation,

500, 502, 981barrier forward contract, 396down-and-inlong, 397, 939

down-and-outlong, 397, 940

up-and-inlong, 397, 935

up-and-outlong, 397, 937

barrier level, 371barrier option, 58, 367, 371down-and-incall, 372, 385put, 372, 387

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N. Privault

down-and-outcall, 372, 381, 395put, 372, 383

in-out parity, 372up-and-incall, 372, 387put, 372, 388

up-and-outcall, 372, 373put, 372, 378

basis point, 640basket option, 443BDT model, 582bear spread option, 267, 872Bermudan swaption, 639Bernoulli distribution, 742Bessel function, 551, 573BGM model, 613, 628binaryoption, 57, 117, 236, 271, 544, 790barrier, 398

tree, 69binary optionAmericanfinite expiration, 508perpetual, 508

binomialdistribution, 742

BIS, 9bisection method, 234, 321bizdays (R package), 222Black(1976) formula, 629caplet formula, 628

Black-Derman-Toy model, 582Black-Scholescalibration, 324formula, 228, 233, 256, 530, 614call option, 207, 629put option, 214, 215, 630

PDE, 205, 227, 234, 392, 395, 720with jumps, 704

bondconvertible, 578convexity, 583duration, 579, 583immunization, 1025ladder, 632option, 542, 625, 1010pricing PDE, 561, 611yield, 570zero-coupon, 558

Borel-Cantelli, 175Borel-Cantelli Lemma, 732

boundary condition, 721break-evenrate, 596, 598strike price, 46underlying asset price, 86, 221

BRENT, 10Bretton Woods, 514bridge model, 616Brownianbridge, 170, 575extrema, 358motion, 131geometric, 244Lévy’s construction, 138, 173, 849series construction, 136, 139

BSDE, 274bull spread option, 267, 872business time, 222butterfly option, 267, 874buy back guarantee, 7, 532buy limit, 463

calendar time, 222callprice, 372, 373, 378

call level, 371call option, 8call spread collar option, 119call swaption, 636call-put parity, 216, 258, 273, 333, 530,

946callablebear contract, 59, 371–373bull contract, 372, 378

Cantor function, 343cap pricing, 630Capital Asset Pricing Model (CAPM),

276, 896caplet pricing, 627cash settlement, 8, 56, 214cash-or-nothing option, 57, 544Category R CBBC, 396cattle futures, 206Cauchydistribution, 739sequence, 833

CBBC, 59, 371–373, 378Category R, 396rebate, 396residual, 396Type N, 372Type R, 372

CBOE, 550Volatility Index®, 334

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Notes on Stochastic Finance

CEV model, 552change of measure, 250change of numéraire, 516, 530characteristicfunction, 754

Chasles relation, 155Chi square distribution, 270, 550, 883Chicago Board Options Exchange, 550chooser option, 273, 888CIR model, 171, 230, 270, 550, 577CKLS, 576Clark-Ocone formula, 100, 419collar option, 10call spread, 119costless, 12put spread, 118

complete market, 33, 38, 253complete space, 146, 153completenesscontinuous time, 186discrete time, 68

compound Poissonmartingale, 690process, 662, 693, 701

compounded yield to maturity, 583compoundinglinear, 594

conditionalexpectation, 60, 747, 756probability, 733

conditioning, 733constant repayment, 48contingent claim, 30, 56, 68, 77attainable, 31, 37, 186

continuous-timelimit, 110

conversion rate, 578convertible bond, 578convexity, 583corportate bond, 578correlationperfect, 610, 619problem, 609

cost of carry, 527costless collar option, 12counterparty risk, 89counting process, 655, 657couponbond, 559rate, 568

Courtadon model, 552, 577Cox process, 659Cox-Ingersoll-Ross model, 171Cox-Ross-Rubinstein model, 69, 208

credit exposure, 89critical price, 502CRR model, 69, 208cumulative distribution function, 738joint, 368, 740

cup & handle, 1

dateof payment, 231of record, 231

deflated price, 516Delta, 90, 92, 204, 209, 211, 217, 219, 233,

237, 263, 874hedging, 262, 537, 539

densityfunction, 737marginal, 369, 741

derivativesfixed income, 621market, 9

derivatives market, 9differential inequalities, 486differential interest rate, 276diffusionelasticicity, 552, 577

digital option, 57, 117, 236, 271, 544, 790discounting, 55, 179lemma, 189, 253

discrete distribution, 742dispersion index, 573, 658distributionBernoulli, 742binomial, 742Cauchy, 739discrete, 742exponential, 739gamma, 739Gaussian, 738geometric, 743Hartman-Watson, 435invariant, 303, 311, 549, 552lognormal, 108, 196, 438, 572, 739, 870marginal, 750negative binomial, 743Pascal, 743Poisson, 743stable, 701stationary, 303, 311, 549, 552uniform, 738

dividend, 115, 123, 231, 268, 457, 503, 506date of payment, 231date of record, 231ex-date, 231payable date, 231

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dollar value, 583dominated convergence theorem, 482, 491Doob-Meyer decomposition, 477Dothan model, 552, 570drawdown option, 426drawdown process, 399drift estimation, 317drifted Brownian motion, 247Dupire PDE, 330duration, 579, 583

early exercise premium, 487ECB, 592effective gearing, 92, 220efficient market hypothesis, 1, 66elasticicity of diffusion, 552, 577elasticity, 221enewal processes, 662entitlement ratio, 9, 212, 217, 326–328equivalent probability measure, 27, 34,

67, 183, 252Esscher transform, 716ETF, 277Euclidean path integral, 575Euler discretization, 724EURIBOR, 594European optionknock-in, 398knock-out, 398

event, 729ex-dividend, 231, 457exchange option, 506, 533exchange-traded fund, 277exercise price, 6exotic option, 58, 83, 260, 367Asian, 427continuous time, 367, 399, 427discrete time, 98lookback option, 399

expectation, 744conditional, 747, 756

exponential distribution, 660, 739exponential Lévy model, 707exponential Vasicek model, 171, 552, 821,

822extrinsic value, 85, 220

face value, 558, 583Fano factor, 573Fatou’s lemma, 243, 467, 733FED, 594Feller condition, 551filtration, 61, 133, 459finite differences

explicit scheme, 718, 720implicit scheme, 719, 722

first theorem of asset pricing, 27, 67, 183,601

fixedincome, 547derivatives, 621

leg, 596rate, 627

floatingleg, 596rate, 627strike, 59

floorlet, 630, 641fOptions (R package), 500, 929, 981foreign exchange, 525option, 528

foreign exchange option, 199formulaLévy-Khintchine, 667smoothing, 668Tanaka, 172, 200, 829, 848Taylor, 866

forwardcontract, 120, 205, 234, 256, 542, 585,

860, 1007American, 510, 998non-deliverable, 206

measure, 579, 622price, 516rate, 585agreement, 585spot, 585–587, 627swap, 595

start option, 268swap rate, 595

forward swapmeasure, 632

four-way zero-collar option, 10Fourier synthesis, 139Fourier transform, 305inversion, 305

FRA, 585Fubini theorem, 670fugazi (the), 320future contract, 206, 795FX option, 199

gains process, 82Galton board, 107Gamma, 219gammaapproximation, 573Greek, 211

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Notes on Stochastic Finance

process, 676gamma distribution, 739gamma function, 739gap, 697Garman-Kohlagen formula, 528Gaussiancumulative distribution function, 112,

626distribution, 207, 738random variable, 755

gearing, 86, 220effective, 92, 220

Geman-Yor method, 437generating function, 171, 754geometricaverage, 429, 455Brownian motion, 192, 244distribution, 743

Girsanov Theorem, 250, 276, 522jump processes, 684, 702

Greeks, 219Delta, 204, 209, 211, 217, 219, 233, 237,

263, 874Gamma, 211, 219Rho, 219Theta, 219, 237, 273, 888Vega, 219, 237, 398, 943

gross market value, 9gross world product, 5, 9guaranteebuy back, 7, 532price lock, 9

GWP, 5

Hartman-Watson distribution, 435Hawaiian option, 428heatequation, 222, 717map, 350

hedge and forget, 205, 795, 1008, 1078hedge ratio, 93, 221hedging, 32, 88, 90, 98, 259change of numéraire, 536mean-variance, 710quantile, 279static, 205, 795, 1008, 1078strategy, 261with jumps, 710

Heston model, 290, 314hexanomial model, 811HIBOR, 594historicalprobability measure, 248volatility, 291, 317

hittingtime, 463

HJMcondition, 601model, 599

Ho-Lee model, 553Hull-White model, 553, 600

immunization, 1025impliedprobability, 16volatility, 320

in the money, 57, 327, 783in-out parity, 372, 946independence, 733, 735, 737, 741, 743,

748, 755, 759independent increments, 242, 686, 687indicator function, 736infimum, 743infinitesimal, 157information flow, 62instantaneous forward rate, 588interest ratedifferential, 276modelaffine, 553Constant Elasticity of Variance, 552Courtadon, 552Cox-Ingersoll-Ross, 270, 550Dothan, 552, 570exponential Vasicek, 171, 552, 821,822

Ho-Lee, 553Hull-White, 553, 600Marsh-Rosenfeld, 552, 577Vasicek, 548, 553

interest rate modelCourtadon, 577Cox-Ingersoll-Ross, 230

intrinsic value, 40, 85, 220invariant distribution, 303, 311, 549, 552inverse Gaussian process, 677IPython notebook, 14, 69, 84, 87, 90, 95,

97, 128, 138, 139, 208, 234, 321, 502,606, 810

Itôformula, 159, 270pathwise, 672with jumps, 673

isometry, 141, 145, 151, 669process, 158, 160, 203, 862stochastic integral, 141, 150, 151, 241table, 162, 403with jumps, 674

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Jamshidian’s trick, 642Jensen’s inequality, 119, 243, 430, 462,

794, 871, 966jointcumulative distribution function, 368,

740probability density function, 740

jump-diffusion process, 697

knock-in option, 398knock-out option, 58, 372, 398Kullback-Leibler entropy, 703kurtosis, 700

Lévyconstruction of Brownian motion, 138,

173, 849process, 676

Lévy-Khintchine formula, 667Lagrangian, 574Laplace transform, 437, 476lawof total expectation, 750of total probability, 731, 734, 750

least square Monte Carlo, 499least square regression, 554legfixed, 596floating, 596

Leibniz integral rule, 601lemmaNeyman-Pearson, 279

leverage, 198, 238, 277, 867, 896liability, 13LIBORmodel, 594rate, 594swap rate, 596, 634, 636

Lipschitz function, 533localtime, 173volatility, 328, 720

logcontract, 235, 269, 315option, 281return, 318dynamics, 192, 708

variance, 108, 196, 288log variance, 196lognormalapproximation, 438distribution, 108, 196, 572, 739, 870

long forward contract, 714, 715lookback option, 399

call, 408put, 399, 402

LSM, 499

Macaulay duration, 583Mandatory Call Event, 396marginaldensity, 369, 741distribution, 750

Margrabe formula, 534mark to market, 39, 68, 78, 206, 254, 795marketcompleteness, 33, 38, 68making, 39price of risk, 246, 252, 309, 561volatility, 309

market terms and data, 85, 218Markov property, 533, 537Marsh-Rosenfeld model, 552, 577martingale, 60, 134, 241, 460compound Poisson, 690continuous time, 182discrete time, 63measurecontinuous time, 181, 701discrete time, 66

method, 252Poisson, 686, 687submartingale, 460supermartingale, 460transform, 64, 242

martingale transform, 64, 82, 464maturity, 6transformation, 586

maximum of Brownian motion, 341MCE, 396meanhitting time, 474reversion, 548

mean square distance, 758measurability, 148Merton model, 709methodbisection, 321Newton-Raphson, 321

Milshtein discretization, 725Minkowski inequality, 146modelBachelier, 191, 230, 236, 269Barone-Adesi & Whaley, 502binomial, 69CKLS, 576hexanomial, 811Hull-White, 553, 600

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Notes on Stochastic Finance

pentanomial, 811trinomial, 74, 112, 125

modifiedBessel function, 551, 573duration, 583

momentgenerating function, 754, 1071

moneyness, 57moving average, 428MPoR, 246, 252, 309, 561Musiela notation, 599

natural logarithm, 207negativebinomial distribution, 743inverse Gaussian process, 678premium, 27risk premium, 182

Nelson-Siegel, 605, 608Newton-Raphson method, 321Neyman-Pearson Lemma, 279nominal value, 583non-deliverable forward contract, 206noncentral Chi square, 270, 550, 883nonlocal operator, 707notional, 597principal, 640, 1044, 1045

notional amount, 9numéraire, 182, 513annuity, 596, 631invariance, 536

numéraire invariance, 537

OLS, 554opening jump, 697optimal stopping, 494optionAsian, 427basket, 444call, 427

at the money, 268barrier, 58, 367basket, 443bear spread, 267, 872binary, 57, 117, 544, 790bull spread, 267, 872butterfly, 267, 874cash-or-nothing, 57, 544chooser, 273, 888digital, 57, 117, 544, 790drawdown, 426effective gearing, 92, 220exotic, 58, 83, 98, 260, 367, 399, 427extrinsic value, 85, 220

foreign exchange, 199forward start, 268gearing, 86, 220Hawaiian, 428intrinsic value, 85, 220issuer, 14, 32knock-out, 58, 372lookback, 399on average, 58, 266, 427, 456on extrema, 368out of the money, 272path-dependent, 98, 260power, 120, 191, 232, 269, 796premium, 32, 86, 221straddle, 892tunnel, 112, 114vanilla, 204variance call, 295variance swap, 292volatility swap, 297writer, 14, 32zero-collar, 10

optionalsampling, 464stopping, 464

order book, 851Ornstein-Uhlenbeck process, 548out of the money, 57, 272

Paley-Wiener series, 139par value, 558, 583paritycall-put, 216, 258, 273, 333, 530, 946in-out, 372, 946

Partial integro-differential equation, 705partition, 734, 756Pascal distribution, 743path freezing, 642path integral, 85, 368, 519, 574Euclidean, 575

path-dependent option, 98, 260pathwise Itô formula, 672payable date, 231payer swap, 596payer swaption, 633payoff function, 7, 9, 367PDEaffine, 305, 553, 1022Black-Scholes, 205, 227Heston, 303integro-differential, 705variational, 497

pentanomial model, 811perfect

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N. Privault

correlation, 610, 619physical delivery, 8, 56, 214PIDE, 705Planck constant, 574Poissoncompound martingale, 662, 701distribution, 743process, 655compound, 693

portfolio, 20process, 82replicating, 90, 95strategy, 31, 50, 77, 184, 187admissible, 181, 186

update, 184, 187value, 54, 78

power option, 120, 191, 232, 269, 796predictable process, 64, 81, 668premiumearly exercise, 487negative, 27option, 86, 221risk, 27, 182, 246

pricecritical, 502graph, 6, 8, 10, 118, 791, 793

price lock guarantee, 9pricing, 77, 83with jumps, 703

principal amount, 640probabilityconditional, 733density function, 737joint, 740

distribution, 737measure, 731equivalent, 27, 34, 67, 183, 252

sample space, 727space, 732

processcounting, 655Cox, 659drawdown, 399gamma, 676inverse Gaussian, 676predictable, 64, 81, 668stable, 676stopped, 464variance gamma, 676

pushforward measure, 690put option, 6put spread collar option, 118put swaption, 638

Python code, 14, 69, 84, 87, 90, 95, 97,128, 138, 139, 208, 234, 321, 502,606, 810

Python packageyfinance, 324

quantile hedging, 279Quantlib, 639quantmod, 202, 318, 472, 556, 592, 678,

697

R code, 10, 137, 138, 140, 143, 149,165–167, 189, 193, 196, 202, 208,210, 215, 222, 231, 234, 249, 302,321, 322, 333, 336, 337, 372, 378,381, 383, 472, 549, 551, 567, 592,639, 661, 662, 664, 677, 678, 687,745, 748, 930, 981

R packagebizdays, 222fOptions, 500, 929, 981quantmod, 202, 318, 472, 556, 592, 678,

697RQuantLib, 639YieldCurve, 592

Radon-Nikodym, 250randomproduct, 752sum, 752variable, 735

rateforward, 585forward swap, 595instantaneous forward, 588LIBOR, 594, 597swap, 596

LIBOR swap, 634, 636swap, 595

realized variance, 291, 318swap, 292

rebate, 372, 373, 378receiver swaption, 638reflection principle, 367relative entropy, 703replicating portfolio, 90, 95replication, 32residual, 372, 373, 378returnlog, 318

Rho, 219Riccati equation, 566, 1027riskcounterparty, 89market price, 246, 252, 309, 561

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Notes on Stochastic Finance

premium, 27, 182risk premium, 246risk-neutral measure, 15, 27, 701continuous time, 181, 246discrete time, 66

riskless asset, 112, 186RQuantLib, 639running maximum, 341, 342

SABR model, 314second theorem of asset pricing, 33, 68,

186self-financing portfoliochange of numéraire, 537continuous time, 184, 185, 187, 188, 710discrete time, 52, 78

sell stop, 463seller swap, 596share right, 25Sharpe ratio, 252SHIBOR, 594short selling, 37, 93, 213ratio, 21

SIBOR, 594singular measure, 404skewness, 700slow-fast system, 309smile, 322smoothing formula, 668spline function, 333spot forward rate, 585–587, 627square-integrablefunctions, 143random variables, 144

St. Petersburg paradox, 746stability warrant, 398stable distribution, 701stable process, 678static hedging, 205, 795, 1008, 1078stationary distribution, 303, 311, 549, 552stochasticcalculus, 156differential equations, 164integral, 80, 139, 148with jumps, 667

integral decomposition, 100, 169, 260,262

process, 50stop-loss/start-gain strategy, 199stopped process, 464stopping time, 462theorem, 464

straddle option, 892Stratonovich integral, 837

strike price, 6, 31floating, 59

string model, 619strong Markov property, 660submartingale, 460super-hedging, 32, 68supermartingale, 460Svensson parametrization, 605swap, 595amortizing, 597measure, 516, 632, 649, 651payer, 596seller, 596variance, 292

swap rate, 595, 597swaption, 633Bermudan , 639

Tanaka formula, 172, 200, 829, 848Taylor’s formula, 157, 866telescoping sum, 598tenor structure, 515, 596, 621terms and data, 85, 218ternary tree, 74, 112, 125theoremasset pricing, 27, 33, 67, 68, 183, 186,

601dominated convergence, 482, 491Fubini, 670Girsanov, 250, 276, 522, 684, 702stopping time, 464

Theta, 219, 237, 273, 888TIBOR, 594timebusiness, 222

time splitting, 199, 270, 847tower property, 63, 65, 81, 82, 87, 153,

241, 243, 262, 265, 517, 561, 750,754, 759, 776, 809

transformEsscher, 716Fourier, 305Laplace, 437, 476martingale, 64, 82, 464

treasury note, 550treebinary, 69ternary, 74, 112, 125

trend estimation, 317triangle inequality, 146triangular arbitrage, 21trinomial model, 74, 112, 125tunnel option, 112, 114turbo warrant, 59, 371–373, 378

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N. Privault

two-factor model, 611Type NCBBC, 372

Type RCBBC, 372

uniform distribution, 738

valuation period, 396vanilla option, 60, 83, 204variable rate, 627variance, 751call option, 295realized, 291, 318swap, 292

variance gamma process, 677variational PDE, 486, 497Vasicek model, 548, 553Vega, 219, 237, 398, 943notional, 292

VIX®, 334volatilityhistorical, 291, 317implied, 320level, 292local, 328, 720

smile, 322surface, 324swap, 297variance swap, 292

warrant, 9, 212stability, 398terms and data, 222turbo, 59, 371–373, 378

West Texas Intermediate (WTI), 5, 10Wiener space, 2

yfinance (Python package), 324yield, 585, 587, 627bond, 570compounded to maturity, 583curve, 586data, 592inversion, 593

YieldCurve (R package), 592

zero measure, 343zero-collar option, 10coupon bond, 558

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Notes on Stochastic Finance

Author index

Achdou, Y. 333Albanese, C. 290, 551Albrecher, H. 305Allegretto, J. 500Applebaum, D. 676Aristotle 5Attari, M. 305

Bachelier, L. 2, 139Barone-Adesi, G. 500, 502Barrieu, P. 435Benth, F.E. 444Bermin, H. 419Björk, T. 41, 607Black, F. 3, 186, 201, 582, 628, 629Bosq, D. 657Boulding, K.E. 187, 514Brace, A. 4, 613Breeden, D.T. 329Brémaud, P. 668Brigo, D. 564, 612, 1023Brown, R. 1Burdzy, K. 342

Carr, P. 294, 314, 436, 437Chan, C.M. 59, 372Chan, K.C. 576Charpentier, A. 592Çınlar, E. 737Cont, R. 667, 676, 683, 689, 697, 713Courtadon, G. 552, 577Cox, J.C. 69, 230, 270, 550Crépey, S. 428Curran, M. 442

Da Fonseca, J. 313Dahl, L. O. 444Dana, R.A. 411Dash, J. 519

Dassios, A. 425Deelstra, G. 444Demeterfi, K. 315Denson, N. 542Derman, E. 315, 330, 582Devore, J.L. 727Di Nunno, G. 98, 260, 713Diallo, I. 444Doob, J.L. 460, 464, 477Dothan, L.U. 552, 570Downes, A. 542Dudley, R.M. 146Dufresne, D. 434, 437Dupire, B. 330Dvoretzky, A. 342

Einstein, A. 2El Karoui, N. 516, 536El Khatib, Y. 419, 422Elliott, R.J. 487, 497, 500Erdos, P. 342Eriksson, J. 59, 372Ewald, C.-O. 457

Faff, R. 1017Feller, W. 290, 551, 883Folland, G.B. 135Föllmer, H. 98, 279Fouque, J.-P. 290, 309Friz, P. 334

Galton, F. 107Gao, M. 313Garman, M.B. 528Gatarek, D. 4, 613Gatheral, J. 309, 313, 334Geman, H. 433, 437, 516, 536, 963Gerber, H.U. 506, 716Glasserman, P. 724Gray, P. 1017

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Guirreri, S. 592

Hagan, P.S. 291, 339, 914Han, J. 313Harrison, J.M. 68, 183, 186Heath, D. 4, 601Heston, S.L. 290, 305Hiriart-Urruty, J.-B. 30Hirsch, F. 144Ho, S.Y. 553Hull, J. 553

Ikeda, N. 151, 243Ingersoll, J.E. 230, 270, 550Itô, K. 3

Jacka, S.D. 498Jacod, J. 727Jaillet, P. 497Jamshidian, F. 536, 625, 642Jarrow, R. 4, 601Jeanblanc, M. 411, 713Joshi, M.S. 542

Kakushadze, Z. 575Kakutani, S. 342Kallenberg, O. 760Kamal, M. 315Kani, I. 330Karolyi, G.A. 576Kemna, A.G.Z. 430Kim, Y.-J. 627Klebaner, F. 277, 897Klebaner, F.C 973Kloeden, P.E. 165Kohlhagen, S.W. 528Kopp, P.E. 487, 497Korn, E. 724Korn, R. 724Kreps, D.M. 68Kroisandt, G. 724Kumar, D. 291, 339, 914

Lacombe, G. 144Lamberton, D. 98, 447, 497Lapeyre, B. 447, 497

Lawi, S. 290, 551Lee, R. 294, 314Lee, S.B. 553Lemaréchal, C. 30Lesniewski, A.S. 291, 339, 914Leukert, P. 279Leung, T. 238Levy, E. 438Li, Y. 313Liinev, J. 444Lim, J.W. 425Lindström, E. 1019Lipton, A. 199Litzenberger, R.h. 329Longstaff, F.A. 499, 501, 576Lyuu, Y.D. 370

Mamon, R.S. 1033Margrabe, W. 534Marsh, T.A. 552, 577Martini, C. 313Matsumoto, H. 434Mayer, P. A. 305Mel~nikov, A.V. 279Menkens, O. 457Mercurio, F. 564, 612, 1023Merton, R.C. 4, 535Meyer, P.A. 477Mikosch, T. 837Milevsky, M.A. 444Milne, J.S. 1083Mörters, P. 343Morton, A. 4, 601Musiela, M. 4, 599, 613

Nechaev, M.L. 279Neuberger, A. 315Nguyen, H.T. 657Nikodym, O.M. 250Norris, J.R. 660Novikov, A. 250

Øksendal, B. 98, 260, 713

Paley, R. 139Papanicolaou, A. 290, 334

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Notes on Stochastic Finance

Papanicolaou, G. 290, 309Peng, S. 274Peres, Y. 343Persson, J. 59, 372Pintoux, C. 571, 572Pironneau, O. 333Pitman, J. 727Platen, E. 165Pliska, S.R. 183, 186Poisson, S.D. 655Prayoga, A. 293, 573Profeta, C. 353Proske, F. 98, 260, 713Protter, P. 159, 164, 250, 262, 522,533, 537, 561, 562, 727

Radon, J. 250Rebonato, R. 291Revuz, D. 135Rochet, J.-C. 516, 536Rogers, C. 449Rosenfeld, E.R. 552, 577Ross, S.A. 69, 230, 270, 550Rouah, F.D. 305Rouault, A. 435Roynette, B. 353Rubinstein, M. 69Rudin, W. 143, 144Ruiz de Chávez, J. 98

Samuelson, P.A. 3Sanders, A.B. 576Santa-Clara, P. 619Sato, K. 690Schied, A. 28, 33, 68, 98, 110Schoenmakers, J. 638, 639Scholes, M. 3, 4, 186, 201Schoutens, W. 305Schröder, M. 436, 437Schwartz, E.S. 499, 501Scorsese, M. 320She, Q.H. 313Shi, Z. 449Shiryaev, A.N. 183, 186

Shiu, E.S.W. 506, 716Shreve, S. 353, 362, 378, 453, 483,503, 545, 932

Sircar, K.R. 290, 309, 334Sircar, R. 238, 309Sølna, K. 290, 309Sornette, D. 619Steele, J.M. 495Stroock, D.W. 758

Tankov, P. 667, 676, 683, 689, 697,713

Teng, T.-R. 536, 629, 638Thales 5Tistaert, J. 305Toy, B. 582Turnbull, S.M. 438

Uy, W.I. 572

Vanmaele, M. 444Vašíček, O. 4, 548, 564Volkov, S.N. 279Vorst, A.C.F. 430

Wakeman, L. 438Watanabe, S. 151, 243Wei, X. 639Whaley, R.E. 500, 502White, A. 553Widder, D.V. 223Wiener, N. 2, 139Williams, D. 98Wilmott, P. 506Wong, H.Y. 59, 372Woodward, D.E. 291, 339, 914Wu, X. 584

Yang, Z. 457Yor, M. 135, 290, 353, 433–435, 437,571, 963

Yu, J.D. 441, 573

Zhang, Q. 313Zou, J. 315

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This book is an introduction to the pricing and hedging of financial deriva-tives, including vanilla and exotic options, by stochastic calculus and partialdifferential equation methods. The presentation is done both in discrete andcontinuous-time financial models, with an emphasis on the complementaritybetween algebraic and probabilistic methods. In particular it covers the pric-ing of some interest rate derivatives, of American options, of exotic optionssuch as barrier, lookback and Asian options, and stochastic models with com-pound Poisson jumps. The text is accompanied with a number of figures andsimulations, and includes numerous examples based on actual market data.The concepts presented are also illustrated by 224 exercises and 13 problemswith complete solutions.

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