an introduction to exotic and path-dependent derivatives

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1、CHAPTER22anintroductiontoexoticandpath-dependentderivativesInthisChapter...•howtoclassifyoptionsaccordingtoimportantfeatures•howtothinkaboutderivativesinawaythatmakesiteasytocompareandcontrastdifferentcontracts•thenamesandcontractdetailsformanybasictypesofexoticoptions22.1INTRODUC

2、TIONThecontractswehaveseensofararethemostbasic,andmostimportant,derivativecontractsbuttheyonlyhintatthefeaturesthatcanbefoundinthemoreinterestingproducts.InthischapterIpreparethewayforthecomplexproductsIwillbediscussinginthenextfewchapters.Exoticoptionsareinterestingforseveralreas

3、ons.Theyarehardertoprice,sometimesbeingverymodel-dependent.Therisksinherentinthecontractsareusuallymoreobscureandcanleadtounexpectedlosses.Carefulhedgingbecomesimportant,whetherdeltahedgingorsomeformofstatichedgingtominimizecashflows.Actually,howtohedgeexoticsisallthatreallymatters

4、.Atradermayhaveagoodideaofareasonablepriceforaninstrument,eitherfromexperienceorbylookingatthepricesofsimilarinstruments.Buthemaynotbesosureabouttherisksinthecontractorhowtohedgethemawaysuccessfully.Itisanimpossibletasktoclassifyalloptions.Thebestthatwecanreasonablyachieveisarough

5、characterizationofthemostpopularofthefeaturestobefoundinderivativeproducts.Ilistsomeofthesefeaturesinthischapterandgiveseveralexamples.InthefollowingfewchaptersIgointomoredetailinthedescriptionoftheoptionsandtheirpricingandhedg-ing.ThefeaturesthatIdescribenowaretimedependence,cash

6、flows,strongpathdependenceandweakpathdependence,dimensionality,the‘order’ofanoption,andfinallyoptionswithembeddeddecisions.368PartTwoexoticcontractsandpathdependencyWearegoingtocontinuewiththeBlack–Scholesthemeforthemomentandshowhowtopriceandhedgeexoticsintheirframework.Theirassumpt

7、ionswillberelaxedinlaterchapters.OneapproachthatIwillnotreallybetakingistotrytodecomposeanexoticintoaportfolioofvanillas.Ifsuchadecompositionisexactthenthecontractwasnotexoticinthefirstplace.(Riddle:Whencanyoudecomposeanexoticintoaportfolioofvanillas?Answer:Whenitisn’texotic.)Youma

8、ygetanideaforanapproximatepricean