資源描述：
《paul wilmott on quantitative finance bonus time》由會員上傳分享，免費在線閱讀，更多相關內容在工程資料-天天文庫。
1、CHAPTER75bonustimeInthisChapter...?modelingthebonuscompensationoftraders?incorporatingaskillfactorintovaluationmodels75.1INTRODUCTIONTradersarecompensatedbytheirbonus,inadditiontotheirbasicsalary.Atypicalbonusstructuremightbetopayout?veortenpercentofth
2、epro?ttheyhavemadeforthebankinthepreviousyear.Thistypeofcompensationhasamajordrawback.Assumingthatthetraderwantstomaximizehisexpectedbonus,thisstructureencourageshimtotakesillyrisks.Forexample,atraderwithanegativetradingaccountwouldtakelargerisksintheh
3、opeofgettinghistradingaccountintotheblack.Ofcourse,thestoryisnotquiteassimpleasthis.Tradershavelimitsimposedontheiravail-ablecapitalandonthegearingandtypeofinstrumentstheyareallowedtotrade.Neverthelesslittleisknownabouthowtorewardagoodtraderoptimally.M
4、ostoftheacademicworkhastakenagame-theoreticapproachbuthasn’tseenmuchuseinpractice.Inthischapterwearegoingtobuildupaframeworkforthestudyofthisproblemandexploreavarietyofpossiblecompensationstructures.Themathematicsofthischapterissimilartothatrequiredint
5、heanalysisofthepassportoption,Chapter27.75.2ONEBONUSPERIODWe’veseentheanalysisoftheproblemofthepassportoptioninChapters27and63.Well,that’sprettymuchthesameasthetraderbonusproblemwhenthebonusisafractionofthe(positivepartofthe)pro?t.Thingsgetmoreinterest
6、ing,andsensibleperhaps,ifthebonusdependsalsoontherealizedSharperatio.WhyshouldabankwanttocompensateatraderdependingonhisSharperatio?Becausethatwaytheyexertsomecontrolovertheriskthatthetradertakes.75.2.1BonusDependingontheSharpeRatioAsalwaysSistheassetp
7、ricefollowingdS=μSdt+σSdX.1176PartFiveadvancedtopicsLetπbethevalueofthetradingaccount.Itfollowsthatdπ=rπdt+q(dS?rSdt),whereqisthepositionofthetrader.Hewillhavesomerestrictionsuchas
8、q
9、≤C,Cisthepositionlimit.LetIbethevarianceofthetradingaccount.Itfollows
10、thattI=q2σ2S2dt0anddI=q2σ2S2dt.Attimet=0,π=I=0andthetraderbeginstotradetheunderlyingasset.Attheendoftheyear,thebankgivestothetraderabonusdependingonthepro?tmade,π(T)andtheSharperatioπ√.II’mignoringtherisk-freeinterestratethatshouldbein
