Preface ........................................................vii
PartIBasicStatisticalMethodsandFinancialApplications
1LinearRegressionModels .................................3
1.1Ordinaryleastsquares(OLS)............................4
1.1.1Residualsandtheirsumofsquares..................4
1.1.2Propertiesofprojectionmatrices....................5
1.1.3Propertiesofnonnegativede?nitematrices...........6
1.1.4StatisticalpropertiesofOLSestimates...............7
1.2Statisticalinference......................................8
1.2.1Con?denceintervals...............................8
1.2.2ANOVA(analysisofvariance)tests..................10
1.3Variableselection........................................12
1.3.1Test-basedandothervariable selectioncriteria........12
1.3.2Stepwisevariableselection..........................15
1.4Regressiondiagnostics...................................16
1.4.1Analysisofresiduals...............................17
1.4.2In?uencediagnostics...............................18
1.5Extensiontostochasticregressors.........................19
1.5.1Minimum-variancelinearpredictors..................19
1.5.2Futuresmarketsandhedgingwithfuturescontracts...20
1.5.3Inferenceinthecaseofstochasticregressors..........21
1.6Bootstrappinginregression...............................22
1.6.1Theplug-inprincipleandbootstrapresampling.......22
1.6.2Bootstrappingregressionmodels....................24
1.6.3Bootstrapcon?denceintervals.......................25
1.7Generalizedleastsquares.................................25
Exercises...................................................135
6DynamicModelsofAsserReturnsandTheirVolatilities ..139
6.1Stylizedfactsontimeseriesofassetreturns.................140
6.2Movingaverageestimatorsoftime-varyingvolatilities........144
6.3Conditionalheteroskedasticmodels........................146
6.3.1TheARCHmodel.................................146
6.3.2TheGARCHmodel...............................147
6.3.3TheintegratedGARCHmodel......................152
6.3.4TheexponentialGARCHmodel.....................152
6.4TheARMA-GARCHandARMA-EGARCHmodels.........155
6.4.1Forecastingfuturereturnsandvolatilities.............156
6.4.2Implementationandillustration.....................156
Exercises...................................................157
PartIIAdvancedTopicsinQuantitativeFinance
7NonparametricRegressionandSubstantive-Empirical
Modeling ..................................................163
7.1Regressionfunctionsandminimum-varianceprediction.......164
7.2Univariatepredictors.....................................165
7.2.1Running-mean/running-linesmoothersandlocal
polynomialregression..............................165
7.2.2Kernelsmoothers..................................166
7.2.3Regressionsplines.................................166
7.2.4Smoothingcubicsplines............................169
7.3Selectionofsmoothingparameter..........................170
7.3.1Thebias-variancetrade-o?.........................170
7.3.2Cross-validation...................................171
7.4Multivariatepredictors...................................172
7.4.1Tensorproductbasisandmultivariateadaptive
regressionsplines..................................172
7.4.2Additiveregressionmodels.........................173
7.4.3Projectionpursuitregression........................174
7.4.4Neuralnetworks...................................174
7.5Amodelingapproachthatcombinesdomainknowledgewith
nonparametricregression.................................176
7.5.1Penalizedsplinemodelsandestimationof
forwardrates.....................................177
7.5.2Asemiparametricpenalizedsplinemodelforthe
forwardratecurveofcorporatedebt.................178
Exercises...................................................179
Contentsxvii
8OptionPricingandMarketData ..........................181
8.1Optionpricesandpricingtheory..........................182
8.1.1Optionsdataandput¨Ccallparity....................18
8.1.2TheBlack-ScholesformulasforEuropeanoptions......183
8.1.3OptimalstoppingandAmericanoptions..............187
8.2Impliedvolatility........................................188
8.3Alternativestoandmodi?cationsoftheBlack-Scholesmodel
andpricingtheory.......................................192
8.3.1Theimpliedvolatilityfunction(IVF)model..........192
8.3.2Theconstantelasticityofvariance(CEV)model......192
8.3.3Thestochasticvolatility(SV)model.................193
8.3.4Nonparametricmethods............................194
8.3.5Acombinedsubstantive-empiricalapproach...........195
Exercises...................................................197
9AdvancedMultivariateandTimeSeriesMethods
inFinancialEconometrics .................................199
9.1Canonicalcorrelationanalysis.............................200
9.1.1Cross-covarianceandcorrelationmatrices.............200
9.1.2Canonicalcorrelations.............................201
9.2Multivariateregressionanalysis...........................203
9.2.1Leastsquaresestimatesinmultivariateregression.....203
9.2.2Reduced-rankregression............................203
9.3Modi?edCholeskydecompositionandhigh-dimensional
covariancematrices......................................205
9.4Multivariatetimeseries..................................206
9.4.1Stationarityandcross-correlation....................206
9.4.2DimensionreductionviaPCA.......................206
9.4.3Linearregressionwithstochasticregressors...........207
9.4.4Unit-roottests....................................211
9.4.5CointegratedVAR.................................213
9.5Long-memorymodelsandregime
switching/structuralchange...............................217
9.5.1Longmemoryinintegratedmodels..................217
9.5.2Change-pointAR-GARCHmodels...................219
9.5.3Regime-switchingmodels...........................224
9.6Stochasticvolatilityandmultivariatevolatilitymodels.......225
9.6.1Stochasticvolatilitymodels.........................225
9.6.2Multivariatevolatilitymodels.......................228
9.7Generalizedmethodofmoments(GMM)...................229
9.7.1Instrumentalvariablesforlinearrelationships.........229
9.7.2Generalizedmomentrestrictionsand
GMMestimation..................................231
9.7.3Anexample:Comparisonofdi?erentshort-term
interestratemodels................................233
Exercises...................................................234
10InterestRateMarkets .....................................239
10.1Elementsofinterestratemarkets..........................240
10.1.1Bankaccount(moneymarketaccount)
andshortrates....................................241
10.1.2Zero-couponbondsandspotrates...................241
10.1.3Forwardrates.....................................244
10.1.4Swapratesandinterestrateswaps..................245
10.1.5Caps,?oors,andswaptions.........................247
10.2Yieldcurveestimation...................................247
10.2.1Nonparametricregressionusingspline
basisfunctions....................................248
10.2.2Parametricmodels.................................248
10.3Multivariatetimeseriesofbondyieldsandother
interestrates............................................252
10.4Stochasticinterestratesandshort-ratemodels..............255
10.4.1Vasicek,Cox-Ingersoll-Ross,andHull-Whitemodels...258
10.4.2Bondoptionprices................................259
10.4.3Black-Karasinskimodel............................260
10.4.4Multifactora?neyieldmodels......................261
10.5StochasticforwardratedynamicsandpricingofLIBORand
swapratederivatives.....................................261
10.5.1StandardmarketformulasbasedonBlack!ˉsmode
offorwardprices..................................262
10.5.2Arbitrage-freepricing:martingalesandnumeraires.....263
10.5.3LIBORandswapmarketmodels....................264
10.5.4TheHJMmodelsoftheinstantaneousforwardrate....266
10.6Parameterestimationandmodelselection..................267
10.6.1Calibratinginterestratemodelsinthe
?nancialindustry..................................267
10.6.2Econometricapproachto?tting
term-structuremodels.............................270
10.6.3Volatilitysmilesandasubstantive-empiricalapproach..271
Exercises...................................................272
11StatisticalTradingStrategies ..............................275
11.1Technicalanalysis,tradingstrategies,
anddata-snoopingchecks.................................277
11.1.1Technicalanalysis.................................277
11.1.2Momentumandcontrarianstrategies................279
11.1.3Pairstradingstrategies.............................279
11.1.4Empiricaltestingofthepro?tability
oftradingstrategies...............................282
11.1.5Valueinvestingandknowledge-based
tradingstrategies..................................285
11.2High-frequencydata,marketmicrostructure,andassociated
tradingstrategies........................................286
11.2.1Institutionalbackgroundandstylizedfactsabout
transactiondata...................................287
11.2.2Bid¨Caskbounceandnonsynchronoustradingmodels...29
11.2.3Modelingtimeintervalsbetweentrades..............292
11.2.4Inferenceonunderlyingpriceprocess................297
11.2.5Real-timetradingsystems..........................299
11.3Transactioncostsanddynamictrading.....................300
11.3.1Estimationandanalysisoftransactioncosts..........300
11.3.2Heterogeneoustradingobjectivesandstrategies.......300
11.3.3Multiperiodtradinganddynamicstrategies...........301
Exercises...................................................302
12StatisticalMethodsinRiskManagement ..................305
12.1Financialrisksandmeasuresofmarketrisk.................306
12.1.1Typesof?nancialrisks.............................306
12.1.2Internalmodelsforcapitalrequirements..............307
12.1.3VaRandothermeasuresofmarketrisk..............307
12.2StatisticalmodelsforVaRandES.........................309
12.2.1TheGaussianconventionandthe t-modi?cation.......309
12.2.2ApplicationsofPCAandanexample................310
12.2.3Timeseriesmodels................................311
12.2.4BacktestingVaRmodels...........................311
12.3Measuringriskfornonlinearportfolios.....................312
12.3.1LocalvaluationviaTaylorexpansions................312
12.3.2FullvaluationviaMonteCarlo......................314
12.3.3Multivariatecopulafunctions.......................314
12.3.4Variancereductiontechniques.......................316
12.4Stresstestingandextremevaluetheory....................318
12.4.1Stresstesting.....................................318
12.4.2Extraordinarylossesandextremevaluetheory........318
12.4.3ScenarioanalysisandMonteCarlosimulations........321
Exercises...................................................321
AppendixA.MartingaleTheoryandCentralLimitTheorems .325
AppendixB.LimitTheoremsforStationaryProcesses.........331
AppendixC.LimitTheoremsUnderlyingUnit-RootTests
andCointegration .........................................333
References.....................................................337
Index ..........................................................349
| 