Risk Measures and Spread

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1、Risk
Measures
Wewillshortlygivedefinitionsofvariousriskmeasures.Thesemeasuresarecalculatedbytradingsoftware'stomanagetheriskininstrumentsandinportfolios.
Thedeltavalueshowsthesensitivityofthepresentvaluetochangesinthemainsourceofriskofaninstrument.Examplesofsourcesofriskareyi

2、eldcurvesandthepricesofunderlyingassetsandthedeltaiscalculatedseparatelyforthese.
Thepricedeltacalculationsareonlyapplicableforderivativeinstrumentswithanunderlyinginstrument,valuedonthebasisofanon-termstructuremodel.Itshowsthechangeintheoreticalpricegivenaunitchangeinthe

3、priceoftheunderlying.Fornon-derivativeinstruments,suchasbonds,adeltapricevalueof1.0isused.ThegeneralDeltaPriceformulais
PVPVU

hPVU*scalepriceUhwhereUisthecurrentvalueofthemainsourceofriskandhisthedifferentiationstep.Whenthemarketpriceoftheunderlyingisused,thepriceshifti

4、sarelativeshift,i.e.h=0.0001xU.Whenatheoreticalunderlyingpriceisused,thepriceshiftisanabsoluteshift,i.e.h=0.01Sometimethisvalueiscalleddeltaexplicit.Example:WewanttocalculatetheDeltaPriceforabondusinga)themarketpriceoftheunderlying,andb)thetheoreticalpriceoftheunderlying.a)Assumet

5、hatthecurrentmarketpriceoftheunderlyingisU=100.17.Thepresentvaluewillnowbecalculatedtwice,thefirsttimeusingthecurrentpriceoftheunderlyingandthesecondtimeafterapplyingashifttothepriceoftheunderlyingwiththeshiftsize124expressedash=Ux0.0001=0.010017.Weobtain:PVU(h)PVU()100priceh

6、NomwhereNomisthenominalamount,typicallyonemillion.b)AssumethatthetheoreticalpriceoftheunderlyingisU=100.15.Theshiftsizeisnowh=0.01andU+h=100.16.Thepresentvalueiscalculatedtwice,usingthesetwodifferentpricesfortheunderlying,whichgivestheresultwiththeformulaabove.
Theyield

7、curvedeltashowsthechangeinthepresentvalue,givenashiftofonebasispointinallyieldcurvesused.Theshiftisappliedtotheannuallycompoundedzerocouponcurve,usingthedaycountfractionAct/365.Theyielddeltacaneitherrefertoanupwardoradownwardshiftofyields.ThegeneralDeltaYieldformulaisPVrhPVr


8、
*scaleyieldwhereh=0.00001andsca