欢迎来到天天文库
浏览记录
ID:7293125
大小:453.65 KB
页数:16页
时间:2018-02-10
《paul wilmott on quantitative finance bonus time》由会员上传分享,免费在线阅读,更多相关内容在工程资料-天天文库。
1、CHAPTER75bonustimeInthisChapter...•modelingthebonuscompensationoftraders•incorporatingaskillfactorintovaluationmodels75.1INTRODUCTIONTradersarecompensatedbytheirbonus,inadditiontotheirbasicsalary.Atypicalbonusstructuremightbetopayoutfiveortenpercentofth
2、eprofittheyhavemadeforthebankinthepreviousyear.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)profit.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,thebankgivestothetraderabonusdependingontheprofitmade,π(T)andtheSharperatioπ√.II’mignoringtherisk-freeinterestratethatshouldbein
此文档下载收益归作者所有