Program Matlab 7.0 Mencari Hampiran Harga Lookback Options

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1 DAFTAR PUSTAKA Hull, John C. Options, Futures, and other Derivatives New Jersey : Prentice Hall Kwok, Yue-Kuen. Mathematical Model of Financial Derivatives Singapore : Springer-Verlag. Ross, Sheldon. An Introduction to Mathematical Finance USA : Cambridge University Press. Taylor, Howard M. and Karlin, Samuel. An Introduction to Stochastic Modeling (Revised Edition) USA : Academic Press. Wheeden, Richard L. and Zygmund, Antoni. Measure and Integral USA : MARCEL DEKKER, INC. 67

2 LAMPIRAN A Date Close 21/06/ /06/ /06/ /06/ /06/ /06/ /06/ /06/ /06/ /06/ /06/ /06/ /06/ /06/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /05/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /03/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /02/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /01/ /12/ /12/ /12/ /12/ /12/ /12/ /12/ /12/ /12/ /12/ /12/ /12/ /12/ /12/ /12/

3 06/12/ /12/ /12/ /12/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /11/ /10/ /10/ /10/ /10/ /10/ /10/ /10/ /10/ /10/ /10/ /10/ /10/ /10/ /10/ /10/ /10/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /09/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /08/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /07/ /06/ /06/ /06/ /06/ /06/ /06/ /06/ /06/

4 LAMPIRAN B Program Matlab 7.0 Mencari Hampiran Harga Lookback Options 1. Penaksiran harga floating lookback options S0 % Harga saham awal N % Jumlah subselang T % Time to Maturity sigma % Standar deviasi harga saham r % Suku bunga dt = T/N; % Time step u = exp(sigma*sqrt(dt)); % Faktor kenaikan d = 1/u; % Faktor penurunan p = (exp(r*dt)-d)/(u-d); % Peluang saham naik q = 1-p; % Peluang saham turun % --- Metode Binomial --- % YP = zeros(n+1,n+1); % Vektor Y(t) untuk put YC = zeros(n+1,n+1); % Vektor Y(t) untuk call VPE = zeros(n+1,n+1); % Matriks binomial opsi put eropa VCE = zeros(n+1,n+1); % Matriks binomial opsi call eropa VPA = zeros(n+1,n+1); % Matriks binomial opsi put amerika VCA = zeros(n+1,n+1); % Matriks binomial opsi call amerika for ia=2:(n+1) for i=1:ia YP(i,ia) YC(i,ia) YC(1,1) = 1; YP(1,1) = 1; = u^(ia-i); = d^(i-1); for ib=1:(n+1) VPE(ib,N+1) = YP(ib,N+1)-1; 70

5 VCE(ib,N+1) = 1-YC(ib,N+1); VPA(ib,N+1) = YP(ib,N+1)-1; VCA(ib,N+1) = 1-YC(ib,N+1); for j=n:-1:2 % keadaan saat t(j) for kp=1:(j-1) VPE(kp,j) = exp(-r*dt)* max((q*vpe(kp,j+1)*d+ p*vpe(kp+2,j+1)*u),0); VPA(kp,j) = max((exp(-r*dt)*(q*vpa(kp,j+1)*d+ p*vpa(kp+2,j+1)*u)),(yp(kp,j)-1)); VPE(j,j) = exp(-r*dt)*max((q*vpe(j,j+1)*d+ p*vpe(j+1,j+1)*u),0); VPA(j,j) = max((exp(-r*dt)*(q*vpa(j,j+1)*d+ p*vpa(j+1,j+1)*u)),(yp(j,j)-1)); VCE(1,j) = exp(-r*dt)*max((q*vce(1,j+1)*d+ p*vce(2,j+1)*u),0); VCA(1,j) = max((exp(-r*dt)*(q*vca(1,j+1)*d+ p*vca(2,j+1)*u)),(1-yc(1,j))); for kc=2:j VCE(kc,j) = exp(-r*dt)*max((q*vce(kc-1,j+1)*d+ p*vce(kc+1,j+1)*u),0); VCA(kc,j) = max((exp(-r*dt)*(q*vca(kc-1,j+1)*d+ p*vca(kc+1,j+1)*u)),(1-yc(kc,j))); VPE(1,1) = exp(-r*dt)*max((q*vpe(1,2)*d+p*vpe(2,2)*u),0); VPA(1,1) = max((exp(-r*dt)*(q*vpa(1,2)*d+p*vpa(2,2)*u)), (YP(1,1)-1)); VCE(1,1) = exp(-r*dt)*max((q*vce(1,2)*d+p*vce(2,2)*u),0); VCA(1,1) = max((exp(-r*dt)*(q*vca(1,2)*d+p*vca(2,2)*u)), (1-YC(1,1))); PutE CallE = VPE(1,1)*S0; = VCE(1,1)*S0; 71

6 PutA CallA = VPA(1,1)*S0; = VCA(1,1)*S0; disp(['nilai Lookback Floating Put Eropa (PutE) num2str(pute)]); disp(['nilai Lookback Floating Call Eropa (CallE) num2str(calle)]); : ', : ', disp('========================================================'); disp('========================================================'); disp(['nilai Lookback Floating Put Amerika (PutA) : ', num2str(puta)]); disp(['nilai Lookback Floating Call Amerika (CallA) : ', num2str(calla)]); disp('========================================================'); 72

7 2. Penaksiran harga fixed lookback options (fixed call) S0 K n r T dt = T/(n-1); % Harga saham awal % Strike Price % Jumlah subselang % Suku bunga % Time to Maturity sigma %Standar deviasi harga saham u = exp(sigma*sqrt(dt)); % Faktor kenaikan d = 1/u; % Faktor penurunan p = (exp(r*dt)-d)/(u-d); % Peluang saham naik q = 1-p; % Peluang saham turun ID = triu(ones(n,n)); j=0; for baris=2:(n-1) for kolom=baris:n j=j+1; if j>baris j=baris; ID(baris,kolom) = j; j=0; sizef = ceil(n/2); F = zeros(n,sizef); %matriks payoff Eropa FA = zeros(n,sizef); %matriks payoff Amerika S = zeros(n,1); for bars=1:n; S(barS,1) = S0*u^(n-barS); for barf=1:n isif = ID(barF,n); js = barf; for kolf=1:isif F(barF,kolF) = max(s(js,1)-k,0); FA(barF,kolF) = max(s(js,1)-k,0); js = js+1; for back=(n-1):-1:2 sizef = ceil(back/2); 73

8 % Matriks evaluasi untuk Amerika------% cekfa = zeros(back,sizef); S = zeros(back,1); for bars=1:back S(barS,1) = S0*u^(back-barS); for barfa=1:back isifa = ID(barFA,back); jsa = barfa; for kolfa=1:isifa cekfa(barfa,kolfa) = max(s(jsa,1)-k); jsa = jsa+1; % Fsem = zeros(back,sizef); FAsem = zeros(back,sizef); ceku = 1; ku = 1; for bku=2:back % barisfsem iku = ID(bku,back); % banyak elemen for barfsem=1:iku ku = ku+1; if barfsem>ceku ku = ku-1; Fsem(bku,barfsem) = exp(-r*dt)*(p*f(bku,ku)+ q*f(bku+1,barfsem)); FAsem(bku,barfsem) = max(exp(-r*dt)*(p*f(bku,ku)+ q*f(bku+1,barfsem)),cekfa(bku,ba rfsem)); ku = 1; ceku = iku; Fsem(1,1) = exp(-r*dt)*(p*f(1,1)+q*f(2,1)); FAsem(1,1) = max(exp(-r*dt)*(p*f(1,1)+q*f(2,1)),cekfa(1,1)); F = zeros(back,sizef); FA = zeros(back,sizef); for tranbf=1:back for trankf=1:sizef F(tranbF,trankF) = Fsem(tranbF,trankF); FA(tranbF,trankF) = FAsem(tranbF,trankF); opsie = exp(-r*dt)*(p*f(1,1)+q*f(2,1)) opsia = exp(-r*dt)*(p*fa(1,1)+q*fa(2,1)) 74

9 (fixed )put S0 K n r T dt = T/(n-1); % Harga saham awal % Strike Price % Jumlah subselang % Suku bunga % Time to maturity sigma %Standar deviasi harga saham u = exp(sigma*sqrt(dt)); % Faktor kenaikan d = 1/u; % Faktor penurunan p = (exp(r*dt)-d)/(u-d); % Peluang saham naik q = 1-p; % Peluang saham turun ID = triu(ones(n,n)); j=0; for baris=2:(n-1) for kolom=baris:n j=j+1; if j>baris j=baris; ID(baris,kolom) = j; j=0; sizef = ceil(n/2); F = zeros(n,sizef); % matriks payoff Eropa FA = zeros(n,sizef); % matriks payoff Amerika S = zeros(n,1); for bars=1:n; S(barS,1) = S0*d^(barS-1); for barf=n:-1:1 isif = ID(barF,n); js = barf; for kolf=1:isif F(barF,kolF) = max(k-s(js,1),0); FA(barF,kolF) = max(k-s(js,1),0); js = js-1; for back=(n-1):-1:2 % step per waktu sizef = ceil(back/2); 75

10 % Matriks evaluasi untuk Amerika % cekfa = zeros(back,sizef); S = zeros(back,1); for bars=1:back S(barS,1) = S0*d^(barS-1); for barfa=back:-1:1 isifa = ID(barFA,back); jsa = barfa; for kolfa=1:isifa cekfa(barfa,kolfa) = max(k-s(jsa,1),0); jsa = jsa-1; % Fsem = zeros(back,sizef); FAsem = zeros(back,sizef); cekd = 1; kd = 1; for bkd=(back-1):-1:1 %step per baris ikd = ID(bkd,back); %jumlah elemen for barfsem=1:ikd kd = kd+1; if barfsem>cekd kd=kd-1; Fsem(bkd,barfsem) = exp(-r*dt)*(p*f(bkd,barfsem)+ q*f(bkd+1,kd)); FAsem(bkd,barfsem) = max(exp(-r*dt)*(p*f(bkd,barfsem) +q*f(bkd+1,kd)), cekfa(bkd,barfsem)); kd = 1; cekd = ikd; Fsem(back,1) = exp(-r*dt)*(p*f(back,1)+q*f(back+1,1)); FAsem(back,1) = max(exp(-r*dt)*(p*f(back,1)+q*f(back+1,1)), cekfa(back,1)); F = zeros(back,sizef); FA = zeros(back,sizef); for tranbf=1:back for trankf=1:sizef F(tranbF,trankF) = Fsem(tranbF,trankF); FA(tranbF,trankF) = FAsem(tranbF,trankF); opsie = exp(-r*dt)*(p*f(1,1)+q*f(2,1)) opsia = exp(-r*dt)*(p*fa(1,1)+q*fa(2,1)) 76

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