兩資產(chǎn)的價差障礙期權(quán)定價分析-資料下載頁
2025-06-16 23:02本頁面
【正文】 arrier%%%%fori=1:nstepforj=1:*(i+1)*(i+2)if(Spread{i,1}(j)=barrier)outbarrier=min(Spread{i,1}(j))。end。if(Spread{i,1}(j)=barrier)inbarrier=max(Spread{i,1}(j))。end。end。end。%%%%%%計算outbarrier期權(quán)價格%%%%%fori=nstep:1:1N=*(i+1)*(i+2)。k=i。forj=*(i+1)*(i+2):1:1if(i==nstep)if(Spread{nstep,1}(j)=outbarrier)Option{nstep,1}(j)=0。elseOption{nstep,1}(j)=max(Spread{nstep,1}(j)strike,0)。end。elseif(Nj=k+1)Option{i,1}(j)=exp(rfrate*dt)*1/3*(Option{i+1,1}(j)+Option{i+1,1}(j+k+1)+Option{i+1,1}(j+k+2))。elsek=k1。N=N(k+2)。Option{i,1}(j)=exp(rfrate*dt)*1/3*(Option{i+1,1}(j)+Option{i+1,1}(j+k+1)+Option{i+1,1}(j+k+2))。end。end。end。end。outprice=exp(rfrate*dt)*1/3*(Option{1,1}(1)+Option{1,1}(2)+Option{1,1}(3))。%%%%計算inbarrier期權(quán)價格%%%%%%fori=nstep:1:1N=*(i+1)*(i+2)。k=i。forj=*(i+1)*(i+2):1:1if(i==nstep)if(Spread{nstep,1}(j)=inbarrier)Option{nstep,1}(j)=0。elseOption{nstep,1}(j)=max(Spread{nstep,1}(j)strike,0)。end。elseif(Nj=k+1)Option{i,1}(j)=exp(rfrate*dt)*1/3*(Option{i+1,1}(j)+Option{i+1,1}(j+k+1)+Option{i+1,1}(j+k+2))。elsek=k1。N=N(k+2)。Option{i,1}(j)=exp(rfrate*dt)*1/3*(Option{i+1,1}(j)+Option{i+1,1}(j+k+1)+Option{i+1,1}(j+k+2))。end。end。end。end。inprice=exp(rfrate*dt)*1/3*(Option{1,1}(1)+Option{1,1}(2)+Option{1,1}(3))。%%%%%%插值計算最終期權(quán)價格%%%%%%option=inprice+(outpriceinprice)*(barrierinbarrier)/(outbarrierinbarrier)；%%%%%%%MC模擬%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%U1=rand(npath,nstep)。U2=rand(npath,nstep)。R=sqrt(2*log(U1))。Theta=2*pi*U2。rand1=R.*cos(Theta)。rand2=R.*sin(Theta)。Payoff=zeros(npath,nstep)。Drift1=(*sigma1^2)*dt。Volatility1=sigma1*sqrt(dt)*rand1。Increments1=Drift1+Volatility1。LogPaths1=cumsum(Increments1,2)+log(X0)。PricePaths1=exp(LogPaths1)。Drift2=(*sigma2^2)*dt。Volatility2=sigma2*sqrt(dt)*(Rho*rand1+sqrt(1Rho^2)*rand2)。Increments2=Drift2+Volatility2。LogPaths2=cumsum(Increments2,2)+log(Y0)。PricePaths2=exp(LogPaths2)。Spread=abs(PricePaths1PricePaths2)。forj=1:npathif(Spread(j,nstep)=barrier)Payoff(j,nstep)=0。elsePayoff(j,nstep)=max(Spread(j,nstep)strike,0)。end。end。mcoption=normfit(mean(exp(rfrate*t)*Payoff(:,nstep)))。end參考文獻：l RenRawChen,SanLinChung,TylerT.YangOptionPricinginaMultiAsset,CompleteMarketEconomy.TheJournalofFinancialandQuantitativeAnalysis,37(2002),649666.l ConvergencefromDiscretetoContinuousTimeContingentClaimsPrices. ReviewofFinancialStudies,3(1990),523546.l Duffie,D.,and.ImplementingArrowDebreuEquilibriabyContinuous TradingofFewLongLivedSecurities.Econometrica,53(1985),13371356
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