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金融商品設計與評價 hw10

金融商品設計與評價 hw10. 計財系大三 林奕全. Outline. 1.CBValue - Putable -Callable - Putable + Callable 2. - Rand+BoxMuller - Halton+BoxMuller:Eur Put. Putable. function [ price,lattice ] = CBValuePut ( s0,r,T,sigma,N,Q,I,P,tau ) deltaT =T/N; u=exp(sigma* sqrt ( deltaT )); d=1/u;

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金融商品設計與評價 hw10

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  1. 金融商品設計與評價hw10 計財系大三 林奕全

  2. Outline • 1.CBValue • -Putable • -Callable • - Putable+ Callable • 2. • -Rand+BoxMuller • -Halton+BoxMuller:Eur Put

  3. Putable • function [ price,lattice ] = CBValuePut( s0,r,T,sigma,N,Q,I,P,tau ) • deltaT=T/N; • u=exp(sigma*sqrt(deltaT)); • d=1/u; • p=(exp(r*deltaT)-d)/(u-d); • lattice=zeros(N+1,N+1); • for j=0:N • lattice(N+1,j+1)=max(I/Q,s0*(u^j)*(d^(N-j))); • end

  4. for i=N-1:-1:0 • for j=0:i • lattice(i+1,j+1)=max(s0*u^(j)*d^(i-j),exp(-r*deltaT)*(p*lattice(i+2,j+2)+(1-p)*lattice(i+2,j+1))); • if i==tau-1 • lattice(i+1,j+1)=max(lattice(i+1,j+1),P/Q); • end • end • end • price=lattice(1,1)*Q;

  5. >> CBValue(35, 0.02, 5, 0.3, 100, 2500, 100000) • ans = • 1.1234e+05 • >> CBValuePut(35, 0.02, 5, 0.3, 100, 2500, 100000,102000,50) • ans = • 1.1399e+05

  6. Callable • function [ price,lattice ] = CBValueCall( s0,r,T,sigma,N,Q,I,C ) • deltaT=T/N; • u=exp(sigma*sqrt(deltaT)); • d=1/u; • p=(exp(r*deltaT)-d)/(u-d); • lattice=zeros(N+1,N+1);

  7. for j=0:N • lattice(N+1,j+1)=max(I/Q,s0*(u^j)*(d^(N-j))); • end • for i=N-1:-1:0 • for j=0:i • lattice(i+1,j+1)=max(s0*u^(j)*d^(i-j),min(exp(-r*deltaT)*(p*lattice(i+2,j+2)+(1-p)*lattice(i+2,j+1)),C/Q)); • end • end • price=lattice(1,1)*Q;

  8. >> CBValue(35, 0.02, 5, 0.3, 100, 2500, 100000) • ans = • 1.1234e+05 • >> CBValueCall(35, 0.02, 5, 0.3, 100, 2500, 100000,102000) • ans = • 9.8619e+04

  9. Putable+ Callable • function [ price,lattice ] = CBValueCallPut( s0,r,T,sigma,N,Q,I,C,P,tau ) • deltaT=T/N; • u=exp(sigma*sqrt(deltaT)); • d=1/u; • p=(exp(r*deltaT)-d)/(u-d); • lattice=zeros(N+1,N+1); • for j=0:N • lattice(N+1,j+1)=max(I/Q,s0*(u^j)*(d^(N-j))); • end

  10. for i=N-1:-1:0 • for j=0:i • lattice(i+1,j+1)=max(s0*u^(j)*d^(i-j),min(exp(-r*deltaT)*(p*lattice(i+2,j+2)+(1-p)*lattice(i+2,j+1)),C/Q)); • if i==tau-1 • lattice(i+1,j+1)=max(lattice(i+1,j+1),P/Q); • end • end • end • price=lattice(1,1)*Q;

  11. >> CBValue(35, 0.02, 5, 0.3, 100, 2500, 100000) • ans = 1.1234e+05=112,340 • >> CBValuePut(35, 0.02, 5, 0.3, 100, 2500, 100000,102000,50) • ans = 1.1399e+05=113,990 • >> CBValueCall(35, 0.02, 5, 0.3, 100, 2500, 100000,102000) • ans = 9.8619e+04=98,619 • >> CBValueCallPut(35, 0.02, 5, 0.3, 100, 2500, 100000,102000,102000,50) • ans = 1.0002e+05=100,020

  12. Halton+BoxMuller:Eur Put • function Seq = GetHalton( HowMany,Base) • Seq=zeros(HowMany,1); • NumBits=1+ceil(log(HowMany)/log(Base)); • VetBase=Base.^(-(1:NumBits)); • WorkVet=zeros(1,NumBits); • for i=1:HowMany • j=1; • ok=0;

  13. while ok==0 • WorkVet(j)=WorkVet(j)+1; • if WorkVet(j)<Base • ok=1; • else • WorkVet(j)=0; • j=j+1; • end • end • Seq(i)=dot( WorkVet,VetBase); • end

  14. function Price = BlshaltonEurPut(s0,X,r,T,sigma,Npoints,Base1,Base2) • nuT=(r-0.5*sigma^2)*T; • siT=sigma*sqrt(T); • H1=GetHalton(ceil(Npoints/2),Base1); • H2=GetHalton(ceil(Npoints/2),Base2); • Vlog=sqrt(-2*log(H1)); • Norm1=Vlog.*cos(2*pi*H2); • Norm2=Vlog.*sin(2*pi*H2); • Norm=[Norm1;Norm2]; • DiscPayoff=exp(-r*T)*max(0,X-s0*exp(nuT+siT*Norm)); • Price=mean(DiscPayoff);

  15. s0=50; • X=52; • r=0.1; • sigma=0.4; • Nrepl=5000; • T=5/12; • Base11=2; • Base12=7; • [Call,Put]=blsprice(s0,X,r,T,sigma); • Halton27=BlshaltonEurPut(s0,X,r,T,sigma,Nrepl,Base11,Base12); • Put • Halton27

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