![泊松分布在金融领域的应用_第1页](http://file4.renrendoc.com/view4/M02/01/2E/wKhkGGaWK0qADOtlAAHuY44NlLs299.jpg)
![泊松分布在金融领域的应用_第2页](http://file4.renrendoc.com/view4/M02/01/2E/wKhkGGaWK0qADOtlAAHuY44NlLs2992.jpg)
![泊松分布在金融领域的应用_第3页](http://file4.renrendoc.com/view4/M02/01/2E/wKhkGGaWK0qADOtlAAHuY44NlLs2993.jpg)
![泊松分布在金融领域的应用_第4页](http://file4.renrendoc.com/view4/M02/01/2E/wKhkGGaWK0qADOtlAAHuY44NlLs2994.jpg)
![泊松分布在金融领域的应用_第5页](http://file4.renrendoc.com/view4/M02/01/2E/wKhkGGaWK0qADOtlAAHuY44NlLs2995.jpg)
版权说明:本文档由用户提供并上传,收益归属内容提供方,若内容存在侵权,请进行举报或认领
文档简介
Random(Poissondistribution)inthefieldoffinancialapplications
【Abstract】mathematicalfinanceasasubject.Usingagreatdealofteachingtheoryandmethodstudyandsolvemajortheoriesinfinancialissues,practicalproblems,andsome,suchasthepricingoffinancialinnovation.Duetofinancialproblemsthecomplexityofthemathematicalknowledge,inadditiontothebaseofknowledge,thereareplentyoftheoriesandmethodsofmodernmathematics.Inthisarticleweintroducethevolumefluctuationsinstockpricemodel.ApplicationofPoissonprocesstheorydescribesthevolatilityofstockprices,andbasedonoptionpricingtheory,Europeancalloptionpricingformulaisderived.Inthecourseoffinancialinvestment,investorstypicallyshyawayfromrisks,andcontroltherisksinthefirstplace,sowefurtherriskaversioninthemarketofEuropeancalloptionspricerange.Inordertogiveinvestorsamorespecificreference.
【Keywords】stochasticprocessofcompoundPoissonprocesssharestradedoptionspricing
Alongwithrapideconomicdevelopment,avarietyoffinancialtoolscontinuetoproduce.Thecorrectvaluationoffinancialinstrumentsisanecessaryconditionforeffectivemanagementofrisk,weusedthepricesofsecuritiesdescribedingeometricBrownianmotionprocessiscontinuous.Withfairpricesandfinancialinstrumentsisthattheyarereasonableandthekey.Mathematicalfinanceis20centurieslaterdevelopedanewcrossdiscipline.Itisobservedwithauniquewaytomeetfinancialproblems,whichcombinemathematicaltoolsandfinancialproblems.Provideabasisforcreativeresearch,solvingfinancialproblemsandguidance.Throughmathematicsbuiltdie,andtheoryanalysis,andtheoryisderived,andnumericalcalculation,quantitativeanalysis,researchandanalysisfinancialtradingintheofvariousproblem,toprecisetodescriptionoutfinancialtradingprocessintheofsomebehaviorandmayofresults,whileresearchitscorrespondingofforecasttheory,reachedavoidedfinancialrisk,andachievedfinancialtradingreturnsmaximizeofpurpose,tomakesaboutfinancialtradingofdecisionmoresimpleandaccurate.
Becauseoffinancialphenomenastudiedinmathematicalfinancestronguncertainty,stochasticprocesstheoryasanimportantbranchofprobabilitytheory,andarewidelyusedinthefinancialresearch.Stochasticprocesstheoryinclude:theoryofprobabilityspaces.Poissonprocess,theupdatingprocess,discreteMarkovchainsandcontinuousparametersoftheMarkovchain,theBrowncampaign,martingalestheoryandstochasticintegration,stochasticdifferentialequations,andsoon.Inrecentdecades,theoryandapplicationsofstochasticprocesseshasbeendevelopingrapidly.Physics,automation,communicationsciences,economicsandManagementSciencesandmanyotherfieldsareactivefigureofthetheoryofstochasticprocesses.
ThisstochasticprocesstheoryofoptionpricingusingPoissonprocesstheorytothestudyofregularityofstockpricefluctuationinthestockmarket,considertheimpactoftransactionsonstockprices,stockpriceprocessmodelisconstructed.Andgivestheoptionofavoidingrisksintheinvestmentprocess.
AndthePoissonprocessconcepts
Definitions1.1randomprocess{Nt,T≥0}iscalledthecountingprocess,iftheIntimeintervals(0,t]occursinacertainevent(duetoapointonthetimelineofevents,sopeoplecalledtheevent)number.Therefore,acountingprocessmustmeet:
(1)NtTakenon-negativeintegervalues;
(2)Ifs<t,thenNs<Nt
(3)NtInR+=[0,∞)Therearecontinuousandpiecewisefetchconstants,
(4)Fors<t,Ns,t=NS-NtIsequaltothetime(s,t]thenumberofeventsoccurringin,
Saidthecountingprocess{Nt,T≥0}hasindependentincrements.Ifit'sinanyfinitenumberofdisjointeventsthatoccurinthetimeintervalofafewindependentofeachother,saidthecountingprocess{Nt,T≥0}withstationaryincrements,ifatanytimetheprobabilitydistributionofthenumberofeventsthatoccurredintheintervaldependsonlyonthelengthoftheinterval,andhasnothingtodowithitslocation.Thatforany0≤t1≤t2Ands≥0IncrementalNt1,t2AndNt1+s,t2+sHavethesameprobabilitydistribution.
Definitions1.2countingprocess{Nt,T≥0}iscalledintensity(orspeed)ThehomogeneousPoissonprocessifitmeetsthefollowingconditions:
(1)P(N0=0)=1,
(2)Hasindependentincrements.
(3)Forany0s<t,Ns,t=NS-NtWithparameter(t--s)ThePoissondistribution,which
Definitions1.3countprocess{,T≥0}iscalledthePoissonprocess,theargumentis,λ>0If
(1)N0=0
;
(2)Processeswithstationaryindependentincrements.
If
Youcanprove
Thatis,Ns+t-NtHasmeanm(t+s)m(t)ofthePoissondistribution.
Non-homogeneousPoissonprocessisimportantbecausenolongerrequiresastationaryincrements,allowingthepossibilityofeventsatcertaintimesthanothers.
Dangstrength(t)Territoriescanbenon-homogeneousPoissonprocessisregarded
③dSprobability
Typeintheαn>0,βn>0,λn>0Marketdepthcorrespondingtotherisk-neutralprobabilitycoefficientindexnsaid"neutral"(neutral).Becausetherisk-neutral,sotheexpectationsofstockyieldsequaltotheyieldsonbonds,namely:
We'vegotaEuropeanbuyingoptionpricingfor:
Four,riskavoidanceandriskcontrol
Onthestockmarket,investorsoftenAvoidRiskandriskcontrolasatoppriority,soconsiderhowtoavoidinvestmentrisksisofgreattheoreticalandpracticalsignificance.Assumetheexpectationsofstockreturnsthanyieldsonbonds,whichu-1αλEξ-(1-d)βλEξ>r
Probabilityisassumedbythemodelshowsthatastock'spricefluctuationsareasfollows:
Undertherisk-neutralprobability,accordingtothemodelassumptions,fluctuationsinstockpriceprobabilityis:
Five,modelthespecificpracticalproblemsofapplication
Select2009years6months22daysuntil2010years6months22daysofchinadotcom(stock)pricesastheresearchobject,theactualdatafromhttp://CN.finance.yahoo.corn。Theyearsharesofthestockpriceandtradingvolumedatastatisticsandanalysis,2010years6months22daysthestock'sopeningpriceof8.57,itsEuropeancalloptionexpirefor3months,2010years9months2
温馨提示
- 1. 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
- 2. 本站的文档不包含任何第三方提供的附件图纸等,如果需要附件,请联系上传者。文件的所有权益归上传用户所有。
- 3. 本站RAR压缩包中若带图纸,网页内容里面会有图纸预览,若没有图纸预览就没有图纸。
- 4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
- 5. 人人文库网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对用户上传分享的文档内容本身不做任何修改或编辑,并不能对任何下载内容负责。
- 6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
- 7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
最新文档
- 清洁公司前台服务心得
- 子女对父母的爱的名言
- 山东省临沂市河东区2023-2024学年小升初易错点数学检测卷含解析
- 小学心理健康教育课学会赞美说课稿
- 土建及安装工程细部做法示意图
- 2024年个人购房按揭抵押合同范例
- 2024年建筑工程施工合同典范文件
- 2024循环经济示范垃圾处理项目承包协议
- 2024年版混凝土施工班组专业劳务服务合同
- 2024年某地区高速公路护坡工程承包协议
- 民法及民事诉讼法练习试卷1(共82题)
- DL∕T 1100.1-2018 电力系统的时间同步系统 第1部分:技术规范
- 健康教育题库
- 2024-2030年甲胺行业市场现状供需分析及重点企业投资评估规划分析研究报告
- 《Excel数据分析》考试复习题库(含答案)
- 完整版施工占道施工方案
- 光伏电站运行、维护协议书
- 二年级下册口算题大全带答案
- 2024年山西焦煤集团有限责任公司校园招聘考试试题参考答案
- (高清版)JTG 3810-2017 公路工程建设项目造价文件管理导则
- 2024时事政治必考试题库(完整版)
评论
0/150
提交评论