目錄
ForewordPreface
Acknowledgments
1Synopsis
PartIFundamentalconceptsoffinance
2Introductiontofinance
2.1Efficientmarket：randomevolutionofsecurities
2.2Financialmarkets
2.3Riskandreturn
2.4Timevalueofmoney
2.5Noarbitrage，martingalesandrisk-neutralmeasure
2.6Hedging
2.7Forwardinterestrates：fixed-incomesecurities
2.8Summary
3Derivativesecurities
3.1Forwardandfuturescontracts
3.2Options
3.3Stochasticdifferentialequation
3.4Itocalculus
3.5Black-Scholesequation：hedgedportfolio
3.6Stockpricewithstochasticvolatility
3.7Merton——Garmanequation
3.8Summary
3.9Appendix：Solutionforstochasticvolatilitywithp=0
PartⅡSystemswithfinitenumberofdegreesoffreedom
4Hamiltoniansandstockoptions
4.1Essentialsofquantummechanics
4.2Statespace：completenessequation
4.3Operators：Hamiltonian
4.4Biack-ScholesandMerton-GarmanHamiltonians
4.5Pricingkernelforoptions
4.6Eigenfunctionsolutionofthepricingkernel
4.7Hamiltonianformulationofthemartingalecondition
4.8Potentialsinoptionpricing
4.9Hamiltonianandbarrieroptions
4.10Summary
4.11Appendix：Two-statequantumsystem（Qubit）
4.12Appendix：Hamiltonianinquantummechanics
4.13Appendix：Down-and-outbarrieroptionspricingkernel
4.14Appendix：Double-knock-outbarrieroptionspricingkernel
4.15Appendix：SchrodingerandBlack-Scholesequations
5Pathintegralsandstockoptions
5.1Lagrangianandactionforthepricingkernel
5.2Black-ScholesLagrangian
5.3Pathintegralsforpath-dependentoptions
5.4Actionforoption-pricingHamiltonian
5.5Pathintegralforthesimpleharmonicoscillator
5.6Lagrangianforstockpricewithstochasticvolatility
5.7Pricingkernelforstockpricewithstochasticvolatility
5.8Summary
5.9Appendix：Path-integralquantummechanics
5.10Appendix：Heisenbergsuncertaintyprincipleinfinance
5.11Appendix：Pathintegrationoverstockprice
5.12Appendix：Generatingfunctionforstochasticvolatility
5.13Appendix：Momentsofstockpriceandstochasticvolatility
5.14Appendix：Lagrangianforarbitraryat
5.15Appendix：Pathintegrationoverstockpriceforarbitraryat
5.16Appendix：MonteCarloalgorithmforstochasticvolatility
5.17Appendix：Mertonstheoremforstochasticvolatility
6StochasticinterestratesHamiltoniansandpathintegrals
6.1SpotinterestrateHamiltonianandLagrangian
6.2Vasicekmodelspathintegral
6.3Heath-Jarrow-Morton（HJM）modelspathintegral
6.4MartingaleconditionintheHJMmodel
6.5PricingofTreasuryBondfuturesintheHJMmodel
6.6PricingofTreasuryBondoptionintheHJMmodel
6.7Summary
6.8Appendix：SpotinterestrateFokker-PlanckHamiltonian
6.9Appendix：Affinespotinterestratemodels
6.10Appendix：Black-Karasinskispotratemodel
6.11Appendix：Black-KarasinskispotrateHamiltonian
6.12Appendix：Quantummechanicalspotratemodels
PartⅢQuantumfieldtheoryofinterestratesmodels
7Quantumfieldtheoryofforwardinterestrates
7.1Quantumfieldtheory
7.2Forwardinterestratesaction
7.3Fieldtheoryactionforlinearforwardrates
7.4ForwardinterestratesvelocityquantumfieldA（t，x）
7.5propagatorforlinearforwardrates
7.6Martingaleconditionandrisk-neutralmeasure
7.7Changeofnumeraire
7.8Nonlinearforwardinterestrates
7.9Lagrangianfornonlinearforwardrates
7.10Stochasticvolatility：functionoftheforwardrates
7.11Stochasticvolatility：anindependentquantumfield
7.12Summary
7.13Appendix：HJMlimitofthefieldtheory
7.14Appendix：Variantsoftherigidpropagator
7.15Appendix：Stiffpropagator
7.16Appendix：Psychologicalfuturetime
7.17Appendix：Generatingfunctionalforforwardrates
7.18Appendix：Latticefieldtheoryofforwardrates
7.19Appendix：ActionS，forchangeofnumeraire
8Empiricalforwardinterestratesandfieldtheorymodels
8.1Eurodollarmarket
8.2Marketdataandassumptionsusedforthestudy
8.3Correlationfunctionsoftheforwardratesmodels
8.4Empiricalcorrelationstructureoftheforwardrates
8.5Empiricalpropertiesoftheforwardrates
8.6Constantrigidityfieldtheorymodelanditsvariants
8.7Stifffieldtheorymodel
8.8Summary
8.9Appendix：Curvatureforstiffcorrelator
9FieldtheoryofTreasurybondsderivativesandhedging
9.1FuturesforTreasuryBonds
9.2OptionpricingforTreasuryBonds
9.3GREEKSfortheEuropeanbondoption
9.4Pricinganinterestratecap
9.5FieldtheoryhedgingofTreasuryBonds
9.6StochasticdeltahedgingofTreasuryBonds
9.7StochastichedgingofTreasuryBonds：minimizingvariance
9.8Empiricalanalysisofinstantaneoushedging
9.9Finitetimehedging
9.10Empiricalresultsforfinitetimehedging
9.11Summary
9.12Appendix：Conditionalprobabilities
9，13Appendix：ConditionalprobabilityofTreasuryBonds
9.14Appendix：HJMlimitofhedgingfunctions
9.15Appendix：StochastichedgingwithTreasuryBonds
9.16Appendix：Stochastichedgingwithfuturescontracts
9.17Appendix：HJMlimitofthehedgeparameters
10FieldtheoryHamiltonianofforwardinterestrates
10.1ForwardinterestratesHamiltonian
10.2Statespacefortheforwardinterestrates
10.3TreasuryBondstatevectors
10.4Hamiltonianforlinearandnonlinearforwardrates
10.5Hamiltonianforforwardrateswithstochasticvolatility
10.6Hamiltonianformulationofthemartingalecondition
10.7Martingalecondition：linearandnonlinearforwardrates
10.8Martingalecondition：forwardrateswithstochasticvolatility
10.9Nonlinearchangeofnumeraire
10.10Summary
10.11Appendix：Propagatorforstochasticvolatility
10.12Appendix：EffectivelinearHamiltonian
10.13Appendix：HamiltonianderivationofEuropeanbondoption
11Conclusions
AMathematicalbackground
A.1Probabilitydistribution
A.2DiracDeltafunction
A.3gaussianintegration
A.4Whitenoise
A.5TheLangevinEquation
A.6Fundamentaltheoremoffinance
A.7Evaluationofthepropagator
Briefglossaryoffinancialterms
Briefglossaryofphysicsterms
Listofmainsymbols
References
Index
前言
Financialmarketshaveundergonetremendousgrowthanddramaticchangesinthepasttwodecades，withthevolumeofdailytradingincurrencymarketshittingoveratrillionUSdollarsandhundredsofbillionsofdollarsinbondandstockmarkets.Deregulationandglobalizationhaveledtolarge-scalecapitalflows;thishasraisednewproblemsforfinanceaswellashasfurtherspurredcompetitionamongbanksandfinancialinstitutions.Theresultingbooms，bubblesandbustsoftheglobalfinancialmarketsnowdirectlyaffectthelivesofhundredsofmillionsofpeople，aswaswitnessedduringthe1998EastAsianfinancialcrisis.
Theprinciplesofbankingandfinancearefairlywellestablished[16，76，87]andthechallengeistoapplytheseprinciplesinanincreasinglycomplicatedenvironment.Theimmensegrowthoffinancialmarkets，theexistenceofvastquantitiesoffinancialdataandthegrowingcomplexityofthemarket，bothinvolumeandsophistication，hasmadetheuseofpowerfulmathematicalandcomputationaltoolsinfinanceanecessity.Inordertomeettheneedsofcustomers，complexfinancialinstrumentshavebeencreated;theseinstrumentsdemandadvancedvaluationandriskassessmentmodelsandsystemsthatquantifythereturnsandrisksforinvestorsandfinancialinstitutions[63，100].
Thewidespreaduseinfinanceofstochasticcalculusandofpartialdifferentialequationsreflectsthetraditionalpresenceofprobabilistsandappliedmathematiciansinthisfield.Thelastfewyearshasseenanincreasinginterestoftheoreticalphysicistsintheproblemsofappliedandtheoreticalfinance.InadditiontotheastCorpusofliteratureontheapplicationofstochasticcalculustofinance，conceptsfromtheoreticalphysicshavebeenfindingincreasingapplicationinboththeoreticalandappliedfinance.Theinfluxofideasfromtheoreticalphysics，asexpressedforexamplein[18]and[69]，hasaddedawholecollectionofnewmathematicalandcomputationaltechniquestofinance，fromthemethodsofclassicalandquantumphysicstotheuseofpathintegration，statisticalmechanicsandsoon.Thisbookispartoftheon-goingprocessofapplyingideasfromphysicstofinance.
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