Asset Pricing in the Derivatives Market----Nizar TOUZI (巴黎高科)

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1、NO-ARBITRAGETHEORYFORDERIVATIVESPRICINGNizarTOUZIEcolePolytechniqueParisDépartementdeMathématiquesAppliquéesnizar.touzi@polytechnique.eduMarch29,2007Contents1Introduction61.1Finitediscrete-timefrictionlessfinancialmarkets........61.1.1Probabilisticsetting...................61.1.2Thefinancialmarket

2、...................71.1.3Self-financingportfoliostrategies............81.1.4Wealthprocess......................91.1.5Changeofnuméraire...................101.2Someexamplesoffrictions....................111.2.1Portfolioconstraints...................111.2.2Solvencyconstraint....................121.2

3、.3Transactioncosts.....................121.2.4Taxesoncapitalgains..................131.2.5Largeinvestorproblem..................131.3Someproblemsinfrictionlessfinancialmarkets.........142Arbitrage-freefrictionlessfinancialmarketsindiscrete-time192.1Thefiniteprobabilityone-periodmodelwithasinglerisk

4、yasset202.2Thefundamentaltheoremofassetpricingingeneralfinitediscrete-timemodels.......................222.2.1Notations.........................222.2.2Reductiontoalocalone-periodproblem........232.2.3Characterizationofthelocalnoarbitragecondition..252.2.4Ondiscrete-timemartingales...............3

5、012.2.5Characterizationofthenoarbitragecondition.....352.3Complement:theclosenessproperty..............382.4Model-freeimplicationsofno-arbitrage.............412.4.1AmericanversusEuropeanoptions...........422.4.2Put-CallParity......................432.4.3Exercisepriceeffects...................432.

6、4.4MaturityEffectsforAmericancallandputoptions..442.4.5BoundsoncallpricesandearlyexerciseofAmericancalls............................452.4.6Riskeffectonoptionsprices...............463Super-hedgingcontingentclaimsindiscrete-timefinancialmarkets483.1Problemformulation.......................483.1.1Defin

7、ition.........................483.1.2Firstproperties......................493.1.3Noarbitragebounds...................503.2One-periodexamples.......................503.2.1Thebinomialmodel...................503.2.2Thetrinomial