pricing and optimal hedging of derivatives, the non-probabilistic model cont’d

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1、CHAPTER69pricingandoptimalhedgingofderivatives,thenon-probabilisticmodelcont’dInthisChapter...•bondoptions•indexamortizingrateswaps•convertiblebonds69.1INTRODUCTIONThischapterstartswithanexaminationofthepricingandhedgingofareal-lifeleasingportfolio.Wethenlookatusingthenon-probabilisticmethodologyf

2、orthepricingandoptimalstatichedgingofavarietyofderivatives.Inparticular,welookatbondoptions,bothEuropeanandAmerican,optionswithcomplexdecisions,indexamortizingrateswapsandconvertibles.Betweenthemthesecontractshaveawidevarietyofinterestingexoticfeatures.69.2AREALPORTFOLIOInFigure69.1areshownthester

3、ling-denominatedcashflowsofDresdner,Kleinwort,Bensonarisingfromaleasingportfolio.Let’sseehowwemightusethemodeltohedgethisportfolio.Firstofall,wewillcalculatethepresentvalueofallthecashflowsusingtheyieldcurvetoday,8thJanuary1998.ThisyieldcurveisshowninFigure69.2.Thepresentvalueisfoundtobe−£3,539,362.

4、Totestthesensitivityofthisvaluetoshiftsintheyieldcurve,IshowinTable69.1thepresentvalueofthecashflowsassuminginstantaneousparallelshiftsintheyieldcurveofvariousmagnitudes.Thesegiveatraditionalwayofdeterminingwhetherornotapositionishedgedagainstmovesintheyieldcurve.Ifwearebeingpessimisticthena2%downw

5、ardshiftintheyieldcurvereducestheportfolio’svalueto−£4,432,153.1100PartFiveadvancedtopics3.E+073.E+072.E+072.E+071.E+075.E+060.E+00−5.E+06−1.E+0709/01/199809/07/199809/01/199909/07/199909/01/200009/07/200009/01/200109/07/200109/01/200209/07/200209/01/200309/07/200309/01/200409/07/200409/01/200509/

6、07/200509/01/200609/07/200609/01/200709/07/2007−2.E+07−2.E+07Figure69.1CashflowsofDresdner,Kleinwort,Benson.87654Yield321Maturity005101520Figure69.2Currentyieldcurve.pricingandoptimalhedgingofderivatives,thenon-probabilisticmodelcont’dChapter691101Table69.1Presentvalueofport-foliowithparallelshifts

7、intheyieldcurve.ShiftincurvePresentvalue(£)2%−2,620,5681%−3,083,0100%−3,539,362−1%−3,989,193−2%−4,432,153Table69.2Benchmarkbonds.CouponMaturityMarketprice(£)1MT-BILL004FEB199899.463MBT-BILL008APR199898.151YGILT12