资源描述：
《3 tree models for stock and options》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、Chapter3TreeModelsforStocksandOptions§1.AStockModelAsbefore,ourstockcanmovetoonlyoneoftwopricesoveroneunitoftime.LetS0=Stockpriceattimet=0wherewherethestockparameters,u,d,andp,aregiven.Weconsiderarepeatedbinomialtreeofthestock.Figure3.1StockpricetreeStockValueProbabilityDenotethes
2、tockpriceattimetbySt,thenItiseasytoobtainthat1.1RecombingTreesThecompressedstocktreeisTimet=0123Ourultimategoalistousesuchtreetopriceoptionsandderivativesandtodescribethebehaviorofportfolios.Theproblem:CanweusethecompressedstocktreetofindE(S3),forexample?1.2ChainingandExpectedValu
3、est=0123Theentryofeachnodehastheform:Sol.Constructthepricetreeforourstockmodel.§2.PricingaEuropeanOptionwiththeTreeModelExample1.AssumeThecalloptionexpiresatt=3.Whatisafairpriceforthecalloptiontoday?Timet=0123Drawtheoptiontree,butweputinonlythevaluesfort=3.Timet=0123Inthefollowing
4、,weusechainingtofilltheblanksinthetree.Supposewearefacedwiththesubtreeasfollows:ThenReturningtotheimmediateexample,wehaveSol.Constructthepricetreeforourstockmodel.Classwork1.AssumeTheputoptionexpiresatt=3.Whatisafairpriceforthederivativetoday?Timet=0123Returningtotheimmediateexamp
5、le,wehaveHomework1.Ex2,Page45Ex3,Page49§3PricinganAmericanOptionAnAmericanoptioncanbeexercisedatanytimepirortoitsexpiration.Howdoes“earlyexercise”affectthevalueoftheoption?Example2.AssumeTheAmericanputoptionexpiresatt=3.WhatisafairpricefortheAmericanputoptiontoday?Sol.Constructthe
6、pricetreeforourstockmodel.Timet=0123Obviously,WenextfillthederivativevalueforjustthelastcolumnTimet=0123ForanAmericanoption,therearetwochoices.Wecouldexercisetheoptionatsomegivenpointorholditforonemoretimeperiod.Ourstrategywillbetoassignvaluestoeachaltern-ativeandthenchoosethemaxi
7、mumforthevalue.ValuefromchainingValuefromimmediateexerciseMaximumofentriesaboveForexample,considerthefollowingsubtree.VNow,wecancompletetheAmericanputoptionvaluetree.Forexample,Classwork2.AssumeTheAmericancalloptionexpiresatt=3.WhatisafairpricefortheAmericancalloptiontoday?Answer.
8、§4.PricingaBarrierOption(1)AKnock
