基于二叉樹模型的期權定價

目錄TOC\o"1-3"\h\u摘要 謝辭及參考文獻謝辭感謝許振宇老師在我選擇課題指導和遇到困難時的幫助；感謝父母一直督促我學習并對我畢業(yè)論文重視和關注；感謝田淼九年以來對我的包容，尤其是大四一年從考研初試到復試再到畢業(yè)設計過程中對我的鼓勵和支持；感謝舍友球王閆申、主任張志鑫、托神劉君敬以及段子手張鴻捷四年來的互相支持，互相幫助，給了我良好的學習環(huán)境和輕松愉快的生活氛圍；感謝以藺平為代表的同組同學及時交流和溝通，使論文內容更加豐富；感謝劉姚睿同學在論文沖刺階段一直替我在圖書館占座；感謝數(shù)學學院2011級野球隊督促我即使在大四也保持體育鍛煉；感謝朋友們讓我在最后一個學期也過著精彩而充實的生活；感謝班長和學委盡職職責地下發(fā)通知督促我的論文及時完成；感謝所有花時間讀到這里的朋友！ 參考文獻[1]OptionsAndOtherJohnC.Hull,Education,8thedition[2] 期權定價的數(shù)學模型和方法（第二版)，姜禮尚，高等教育出版社[3] 基于二叉樹模型亞式期權定價的研究，岳研，中南大學碩士學位論文2007[4] Thepricingofoptionsandcorporateliabilities,andJournalof81:635-654,1973[5] 期權定價實驗教程，宋斌，清華大學出版社，2014[6] ComputationalStatistics,GeofandJenniferA.Hoeting,Wiley-[7] Theoryofrationaloptionpricing,R.C.Merton,BellJournalofEconomicsandScience,4:141-183,1973[8] MathematicsofFinancialR.J.ElliottandSpringerNew1999[9] toCalculusAppliedtoFinance,andB.Lapeyre,Chapman&Hall,London,1996[10]forComputationalFinance,R.Seydel,2002[11][12]TheArtofComputerProgrammingAlgorithms,Reading,MA,3rdedition,1997[13]期權價格波動率與定價理論，謝爾登·納坦恩伯格，經(jīng)濟科學出版社，2000[14]ThesqueezemethodforgenerationgammaG.Marsaglia,ComputersandMathematicswithApplications,3:321-325,1997[15]Fundamentalsoftheoptionsmarket，MichaelS.Williams，AmyS.Hoffman，楊睿譯，機械工業(yè)出版社，2012[16]Simulation,S.M.Ross,AcademicPress,SanDiego,CA,2ndedition,1997附錄計算過程中涉及算法A.二叉樹模擬s=50k=20r=0.1theta=0.4t=5/12q=0kz=1y=c()for(nin1:50){u=exp(theta*(t/n)^0.5)d=1/ua=exp((r-q)*(t/n))p=(a-d)/(u-d)stock=matrix(0,n+1,n+1)option=matrix(0,n+1,n+1)stock[1,1]=sfor(iin2:(n+1)){for(jin1:i){if(j<=i/2)stock[i,j]=stock[i-1,j]*uelsestock[i,j]=stock[i-1,j-1]*d}}for(iin1:(n+1)){if(kz==1){if(stock[n+1,i]<=k)option[n+1,i]=0elseoption[n+1,i]=stock[n+1,i]-k}else{if(stock[n+1,i]>=k)option[n+1,i]=0elseoption[n+1,i]=k-stock[n+1,i]}}for(iinn:1){for(jin1:i)option[i,j]=(option[i+1,j]*p+option[i+1,j+1]*(1-p))*exp(-r*t/n)}print(option[1,1])x=c(1:n)y[n]=option[1,1]plot(x,y,main="二叉樹方法模擬期權定價",xlab="步數(shù)",ylab="期權價格",type="b")}d1=(log(s/k)+(r+theta^2)/t)/(theta*sqrt(t))d2=d1-theta*sqrt(t)c=s*pnorm(d1)-k*pnorm(d2)*exp(-r*t)c

B.三叉樹模擬s=50k=49r=0.1theta=0.4t=5/12q=0kz=1y=c()for(nin1:50){u=exp(theta*(3*t/n)^0.5)d=1/upd=-sqrt(t/n/12/theta^2)*(r-q-1/2*theta^2)+1/6pm=2/3pu=sqrt(t/n/12/theta^2)*(r-q-1/2*theta^2)+1/6stock=matrix(0,n+1,2*n+1)option=matrix(0,n+1,2*n+1)stock[1,1]=sfor(iin2:(n+1)){for(jin1:(2*i-1)){if(j<=i)stock[i,j]=stock[i-1,j]*uelsestock[i,j]=stock[i-1,j-2]*d}}for(jin1:(2*n+1)){if(kz==1){if(stock[n+1,j]<=k)option[n+1,j]=0elseoption[n+1,j]=stock[n+1,j]-k}else{if(stock[n+1,j]>=k)option[n+1,j]=0elseoption[n+1,j]=k-stock[n+1,j]}}for(iinn:1){for(jin1:(2*i-1))option[i,j]=(option[i+1,j]*pu+option[i+1,j+1]*pm+option[i+1,j+2]*pd)*exp(-r*t/n)}print(option[1,1])x=c(1:n)y[n]=option[1,1]pl