Institutional Repository | Satya Wacana Christian University: Perhitungan Harga Opsi Eropa Menggunakan Metode Gerak Brown Geometrik
Lampiran 1
Tabel 1. data harga saham penutupan harian dari PT. HM. Sampoerna Tbk. tanggal 1 Maret 2010 sampai 29
Februari 2012
Date
3/1/2010
3/2/2010
3/3/2010
3/4/2010
3/5/2010
3/8/2010
3/9/2010
3/10/2010
3/11/2010
3/12/2010
3/15/2010
3/17/2010
3/18/2010
3/19/2010
3/22/2010
3/23/2010
3/24/2010
3/25/2010
3/26/2010
3/29/2010
3/30/2010
3/31/2010
4/1/2010
4/5/2010
4/6/2010
4/7/2010
4/8/2010
4/9/2010
4/12/2010
4/13/2010
4/14/2010
4/15/2010
4/16/2010
4/19/2010
4/20/2010
4/21/2010
Close
13200
13200
13200
13200
13200
13200
13250
13900
13500
13500
13500
13700
13600
13650
13550
13400
13400
13400
13900
14000
14050
13950
13900
13800
13800
13850
13850
13800
13800
13800
13800
13950
13750
13700
13700
13700
5/6/2010
5/7/2010
5/10/2010
5/11/2010
5/12/2010
5/14/2010
5/17/2010
5/18/2010
5/19/2010
5/20/2010
5/21/2010
5/24/2010
5/25/2010
5/26/2010
5/27/2010
5/31/2010
6/1/2010
6/2/2010
6/3/2010
6/4/2010
6/7/2010
6/8/2010
6/9/2010
6/10/2010
6/11/2010
6/14/2010
6/15/2010
6/16/2010
6/17/2010
6/18/2010
6/21/2010
6/22/2010
6/23/2010
6/24/2010
6/25/2010
6/28/2010
13550
14400
14500
14300
14550
14350
14400
14550
14150
14250
14200
14250
13800
14900
14550
14650
14500
14400
14600
14700
14700
14950
15000
15200
15500
15050
15350
15100
15150
16200
17950
19100
19000
18750
18900
18900
1
7/13/2010
7/14/2010
7/15/2010
7/16/2010
7/19/2010
7/20/2010
7/21/2010
7/22/2010
7/23/2010
7/26/2010
7/27/2010
7/28/2010
7/29/2010
7/30/2010
8/2/2010
8/3/2010
8/4/2010
8/5/2010
8/6/2010
8/9/2010
8/10/2010
8/11/2010
8/12/2010
8/13/2010
8/16/2010
8/18/2010
8/19/2010
8/20/2010
8/23/2010
8/24/2010
8/25/2010
8/26/2010
8/27/2010
8/30/2010
8/31/2010
9/1/2010
18800
19000
18700
18900
18850
19100
19150
18950
19000
19000
18950
18950
19000
19100
18900
18850
19000
19000
18850
18850
18700
18600
18900
19000
18800
18800
18900
19000
20100
19550
19750
19950
19900
19850
19800
19850
4/22/2010
4/23/2010
4/26/2010
4/27/2010
4/28/2010
4/29/2010
4/30/2010
5/3/2010
5/4/2010
5/5/2010
9/23/2010
9/24/2010
9/27/2010
9/28/2010
9/29/2010
9/30/2010
10/1/2010
10/4/2010
10/5/2010
10/6/2010
10/7/2010
10/8/2010
10/11/2010
10/12/2010
10/13/2010
10/14/2010
10/15/2010
10/18/2010
10/19/2010
10/20/2010
10/21/2010
10/22/2010
10/25/2010
10/26/2010
10/27/2010
10/28/2010
10/29/2010
11/1/2010
11/2/2010
11/3/2010
11/4/2010
13700
13700
13850
13850
13750
13850
14000
13950
14100
13000
20250
20900
21750
21950
21850
22000
21750
21700
21700
21500
21500
21350
21800
21550
21650
21450
21350
21450
21300
21350
21400
21300
21350
21250
21200
21400
21450
21300
24150
28400
27500
6/29/2010
6/30/2010
7/1/2010
7/2/2010
7/5/2010
7/6/2010
7/7/2010
7/8/2010
7/9/2010
7/12/2010
11/30/2010
12/1/2010
12/2/2010
12/3/2010
12/6/2010
12/8/2010
12/9/2010
12/10/2010
12/13/2010
12/14/2010
12/15/2010
12/16/2010
12/17/2010
12/20/2010
12/21/2010
12/22/2010
12/23/2010
12/27/2010
12/28/2010
12/29/2010
12/30/2010
1/3/2011
1/4/2011
1/5/2011
1/6/2011
1/7/2011
1/10/2011
1/11/2011
1/12/2011
1/13/2011
1/14/2011
18500
18650
18400
18400
18500
19100
18800
18950
19350
18800
27500
27500
27750
27800
28000
27950
28450
29050
29100
28850
28550
29050
29000
28500
28500
28300
28200
28400
28600
28900
28150
28000
27800
27700
27600
27500
26850
26700
26900
26700
26500
2
9/2/2010
9/3/2010
9/6/2010
9/7/2010
9/15/2010
9/16/2010
9/17/2010
9/20/2010
9/21/2010
9/22/2010
2/9/2011
2/10/2011
2/11/2011
2/14/2011
2/16/2011
2/17/2011
2/18/2011
2/21/2011
2/22/2011
2/23/2011
2/24/2011
2/25/2011
2/28/2011
3/1/2011
3/2/2011
3/3/2011
3/4/2011
3/7/2011
3/8/2011
3/9/2011
3/10/2011
3/11/2011
3/14/2011
3/15/2011
3/16/2011
3/17/2011
3/18/2011
3/21/2011
3/22/2011
3/23/2011
3/24/2011
20450
21250
21800
21550
20900
20850
20550
20350
20300
20250
25500
25350
25250
25700
25300
25250
25450
25800
25700
25750
25400
25750
25700
25400
25400
25350
25400
25450
25400
25400
25350
25100
25350
25350
25500
25400
25950
25950
25950
26500
26400
11/5/2010
11/8/2010
11/9/2010
11/10/2010
11/11/2010
11/12/2010
11/15/2010
11/16/2010
11/18/2010
11/19/2010
11/22/2010
11/23/2010
11/24/2010
11/25/2010
11/26/2010
11/29/2010
4/18/2011
4/19/2011
4/20/2011
4/21/2011
4/25/2011
4/26/2011
4/27/2011
4/28/2011
4/29/2011
5/2/2011
5/3/2011
5/4/2011
5/5/2011
5/6/2011
5/9/2011
5/10/2011
5/11/2011
5/12/2011
5/13/2011
5/16/2011
5/18/2011
5/19/2011
5/20/2011
5/23/2011
5/24/2011
26150
26150
27000
26900
27800
28000
27950
27650
27600
27800
28150
28000
27550
28050
28000
27600
28000
28000
28000
28000
28000
28000
28000
28000
28000
28000
27950
27900
27800
27800
27750
27850
27900
27900
28000
27950
28000
28700
28800
28500
28600
1/17/2011
1/18/2011
1/19/2011
1/20/2011
1/21/2011
1/24/2011
1/25/2011
1/26/2011
1/27/2011
1/28/2011
1/31/2011
2/1/2011
2/2/2011
2/4/2011
2/7/2011
2/8/2011
6/27/2011
6/28/2011
6/30/2011
7/1/2011
7/4/2011
7/5/2011
7/6/2011
7/7/2011
7/8/2011
7/11/2011
7/12/2011
7/13/2011
7/14/2011
7/15/2011
7/18/2011
7/19/2011
7/20/2011
7/21/2011
7/22/2011
7/25/2011
7/26/2011
7/27/2011
7/28/2011
7/29/2011
8/1/2011
26500
26500
26200
26000
26000
25900
25900
25400
25450
25600
25500
25350
25650
25600
25550
25500
28000
28300
28600
29000
28700
28800
28700
28750
29100
29200
29000
29300
29400
30150
30000
30050
30100
30300
31000
31000
30900
31200
31250
32000
32200
3
3/25/2011
3/28/2011
3/29/2011
3/30/2011
3/31/2011
4/1/2011
4/4/2011
4/5/2011
4/6/2011
4/7/2011
4/8/2011
4/11/2011
4/12/2011
4/13/2011
4/14/2011
4/15/2011
9/9/2011
9/12/2011
9/13/2011
9/14/2011
9/15/2011
9/16/2011
9/19/2011
9/20/2011
9/21/2011
9/22/2011
9/23/2011
9/26/2011
9/27/2011
9/28/2011
9/29/2011
9/30/2011
10/3/2011
10/4/2011
10/5/2011
10/6/2011
10/7/2011
10/10/2011
10/11/2011
10/12/2011
10/13/2011
26400
26100
25900
26100
26200
26500
30750
28550
28600
28300
28250
28350
28400
28150
28350
28350
32850
32250
32250
32000
31700
31900
31700
31500
31700
28500
29750
28950
30100
29900
30000
30100
29550
29200
29400
30000
30100
29550
30650
30700
30950
5/25/2011
5/26/2011
5/27/2011
5/30/2011
5/31/2011
6/1/2011
6/3/2011
6/6/2011
6/7/2011
6/8/2011
6/9/2011
6/10/2011
6/13/2011
6/14/2011
6/15/2011
6/16/2011
6/17/2011
6/20/2011
6/21/2011
6/22/2011
6/23/2011
6/24/2011
11/15/2011
11/16/2011
11/17/2011
11/18/2011
11/21/2011
11/22/2011
11/23/2011
11/24/2011
11/25/2011
11/28/2011
11/29/2011
11/30/2011
12/1/2011
12/2/2011
12/5/2011
12/6/2011
12/7/2011
12/8/2011
12/9/2011
28600
28800
29000
28900
28950
29150
29000
29000
29100
29400
29100
29200
28250
28250
28100
28050
27950
28000
28000
28050
28150
28200
34050
33700
34900
35700
37000
38400
37500
37100
37450
37500
39100
39000
39200
39300
39000
38800
38850
38750
38750
8/2/2011
8/3/2011
8/4/2011
8/5/2011
8/8/2011
8/9/2011
8/10/2011
8/11/2011
8/12/2011
8/15/2011
8/16/2011
8/18/2011
8/19/2011
8/22/2011
8/23/2011
8/24/2011
8/25/2011
8/26/2011
9/5/2011
9/6/2011
9/7/2011
9/8/2011
1/20/2012
1/24/2012
1/25/2012
1/26/2012
1/27/2012
1/30/2012
1/31/2012
2/1/2012
2/2/2012
2/3/2012
2/6/2012
2/7/2012
2/8/2012
2/9/2012
2/10/2012
2/13/2012
2/14/2012
2/15/2012
2/16/2012
32100
31950
32550
31500
31100
30950
31500
31500
31300
31400
31400
31400
31100
31100
30900
30950
30950
31000
31500
31600
32000
32800
42100
42500
42500
43000
42950
42400
42500
42800
44000
45000
46500
46750
46750
46600
46500
47500
47300
47900
47900
4
10/14/2011
10/17/2011
10/18/2011
10/19/2011
10/20/2011
10/21/2011
10/24/2011
10/25/2011
10/26/2011
10/27/2011
10/28/2011
10/31/2011
11/1/2011
11/2/2011
11/3/2011
11/4/2011
11/7/2011
11/8/2011
11/9/2011
11/10/2011
11/11/2011
11/14/2011
3/29/2012
3/30/2012
4/2/2012
4/3/2012
4/4/2012
4/5/2012
4/9/2012
4/10/2012
4/11/2012
4/12/2012
4/13/2012
4/16/2012
4/17/2012
4/18/2012
4/19/2012
4/20/2012
4/23/2012
4/24/2012
4/25/2012
30750
31000
30900
31150
31000
31300
31500
31500
31500
31950
31800
31650
31550
31900
31850
32250
32300
32200
32550
32200
32200
32750
52900
53200
53500
54050
54200
54300
54200
54300
53900
54000
54150
54200
54000
54350
54350
54400
54300
54350
54300
12/12/2011
12/13/2011
12/14/2011
12/15/2011
12/16/2011
12/19/2011
12/20/2011
12/21/2011
12/22/2011
12/23/2011
12/27/2011
12/28/2011
12/29/2011
12/30/2011
1/2/2012
1/3/2012
1/4/2012
1/5/2012
1/6/2012
1/9/2012
1/10/2012
1/11/2012
1/12/2012
1/13/2012
1/16/2012
1/17/2012
1/18/2012
1/19/2012
38700
38950
38850
38700
38550
38600
38500
38500
38500
38500
38500
38500
38650
39000
39000
39000
39800
40000
39550
39950
40250
41800
42200
42350
42000
42000
42000
42250
2/17/2012
2/20/2012
2/21/2012
2/22/2012
2/23/2012
2/24/2012
2/27/2012
2/28/2012
2/29/2012
3/1/2012
3/2/2012
3/5/2012
3/6/2012
3/7/2012
3/8/2012
3/9/2012
3/12/2012
3/13/2012
3/14/2012
3/15/2012
3/16/2012
3/19/2012
3/20/2012
3/21/2012
3/22/2012
3/26/2012
3/27/2012
3/28/2012
47700
47700
47700
48800
53000
53000
52050
52850
53000
52500
53000
52800
52850
52950
53500
53100
52900
52800
52850
52850
52650
53000
52950
52800
52750
52650
52650
52750
4/26/2012
4/27/2012
4/30/2012
5/1/2012
5/2/2012
5/3/2012
5/4/2012
5/7/2012
5/8/2012
5/9/2012
5/10/2012
5/11/2012
5/14/2012
5/16/2012
5/21/2012
5/22/2012
5/23/2012
5/24/2012
5/25/2012
5/28/2012
5/29/2012
5/30/2012
5/31/2012
54350
54350
54200
54250
54600
54800
55700
55700
55500
55500
55700
55750
55000
54000
54000
53750
52700
53100
53000
53100
53100
53000
52800
Lampiran 2
Algoritma Matlab untuk menampilkan data dan return dari harga saham penutupan PT.
HM. Sampoerna. Tbk adalah sebagai berikut :
Saham=csvread('HMSP.csv');
n=length(Saham);
figure(1)
plot(1:n,Saham)
title('Harga Saham Penutupan Harian PT. HM Sampoerna')
xlabel('waktu (t)'), ylabel('Harga Saham')
Ret=diff(log(Saham));
n_Ret=length(Ret);
5
figure(2)
plot(1:n_Ret,Ret)
title('Nilai Return dari Harga Saham')
ylabel('Return Harga Saham')
Algritma Matlab untuk estimasi parameter adalah sebagai berikut :
Saham=csvread('HMSP.csv');
ndat=length(Saham);
Ret=diff(log(Saham));
n_Ret=length(Ret);
myu_MLE=sum(Ret)/(ndat-1);
sigma_MLE=sqrt((sum((Ret-myu_MLE).^2))/(ndat-1));
Algoritma Matlab untuk simulasi harga saham untuk satu tahun kedepan adalah sebagai
berikut:
clc
clear all
%---Parameter-parameter metode.
S0=53000; r=0.0575; T=1; n=269; M=100;
%---Inisialisasi.
estimasi;
S=zeros(M,n);
S(:,1)=S0;
dt=T/n; % time-step
t=(0:dt:n*dt); % vektor titik waktu
%---Harga-harga aset pada setiap simulasi.
randn('state',100);
for m=1:M
for i=1:n
S(m,i+1)=S(m,i)*exp((r-0.5*sigma_MLE^2)*dt+(sigma_MLE*sqrt(dt))*randn);
end
figure(1)
plot(t,S(m,:),'-'), hold on
end
hold off
xlabel('waktu'), ylabel('Harga Saham')
title('Simulasi Pergerakan Harga Saham')
figure(2)
plot(1:M,S(:,n+1),'-')
xlabel('simulasi'), ylabel('Harga Saham')
title('Simulasi Harga Saham Saat Satu Tahun Kedepan')
6
Algoritma Matlab untuk menentukan harga opsi adalah sebagai berikut:
St=S(:,n+1);
%Nilai Opsi Call Eropa
K = [50000 53000 56000];
for i = 1:3
C(i)=(sum(exp(-r*T)*max(0,St-K(i))))./M;
end
%Nilai Opsi Call Eropa
for i = 1:3
P(i)=(sum(exp(-r*T)*max(0,K(i)-St)))./M;
end
[K' C' P']
Algoritma Matlab untuk simulasi pergerakan harga saham tiga bulan kedepan serta
mendapatkan nilai prosentase nilai error yang maksimum adalah sebagai berikut:
clc
clear all
%---Parameter-parameter metode.
S0=53000; T=1/4; n=61; M=100;
%---Inisialisasi.
estimasi;
S=zeros(M,n);
galat=zeros(1,n);
S(:,1)=S0;
dt=T/n; % time-step
t=(0:dt:n*dt); % vektor titik waktu
%---Harga-harga aset pada setiap simulasi.
randn('state',100);
for m=1:M
for i=1:n
S(m,i+1)=S(m,i)*exp((myu_MLE-0.5*sigma_MLE^2)*dt+(sigma_MLE*sqrt(dt))*randn);
end
figure(1)
plot(t,S(m,:),'-'), hold on
end
hold off
xlabel('waktu(Tahun)'), ylabel('Harga Saham(Rupiah)')
title('Simulasi Pergerakan Harga Saham')
%studi error dari simulasi
data2=csvread('HMSP2.csv')';
galat=(abs((mean(S))'-data2')./data2')*100;
max(galat)
7
figure(2)
plot(data2)
xlabel('waktu(Hari)'), ylabel('Harga Saham')
title('Harga Saham PT. HM Sampoerna Tbk. tanggal 29 Februari sampai 31 Mei 2012')
figure(3)
plot(galat)
xlabel('waktu(Hari)'), ylabel('Error Dari Simulasi (dalam persen)')
title('Studi Error')
8
Tabel 1. data harga saham penutupan harian dari PT. HM. Sampoerna Tbk. tanggal 1 Maret 2010 sampai 29
Februari 2012
Date
3/1/2010
3/2/2010
3/3/2010
3/4/2010
3/5/2010
3/8/2010
3/9/2010
3/10/2010
3/11/2010
3/12/2010
3/15/2010
3/17/2010
3/18/2010
3/19/2010
3/22/2010
3/23/2010
3/24/2010
3/25/2010
3/26/2010
3/29/2010
3/30/2010
3/31/2010
4/1/2010
4/5/2010
4/6/2010
4/7/2010
4/8/2010
4/9/2010
4/12/2010
4/13/2010
4/14/2010
4/15/2010
4/16/2010
4/19/2010
4/20/2010
4/21/2010
Close
13200
13200
13200
13200
13200
13200
13250
13900
13500
13500
13500
13700
13600
13650
13550
13400
13400
13400
13900
14000
14050
13950
13900
13800
13800
13850
13850
13800
13800
13800
13800
13950
13750
13700
13700
13700
5/6/2010
5/7/2010
5/10/2010
5/11/2010
5/12/2010
5/14/2010
5/17/2010
5/18/2010
5/19/2010
5/20/2010
5/21/2010
5/24/2010
5/25/2010
5/26/2010
5/27/2010
5/31/2010
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Lampiran 2
Algoritma Matlab untuk menampilkan data dan return dari harga saham penutupan PT.
HM. Sampoerna. Tbk adalah sebagai berikut :
Saham=csvread('HMSP.csv');
n=length(Saham);
figure(1)
plot(1:n,Saham)
title('Harga Saham Penutupan Harian PT. HM Sampoerna')
xlabel('waktu (t)'), ylabel('Harga Saham')
Ret=diff(log(Saham));
n_Ret=length(Ret);
5
figure(2)
plot(1:n_Ret,Ret)
title('Nilai Return dari Harga Saham')
ylabel('Return Harga Saham')
Algritma Matlab untuk estimasi parameter adalah sebagai berikut :
Saham=csvread('HMSP.csv');
ndat=length(Saham);
Ret=diff(log(Saham));
n_Ret=length(Ret);
myu_MLE=sum(Ret)/(ndat-1);
sigma_MLE=sqrt((sum((Ret-myu_MLE).^2))/(ndat-1));
Algoritma Matlab untuk simulasi harga saham untuk satu tahun kedepan adalah sebagai
berikut:
clc
clear all
%---Parameter-parameter metode.
S0=53000; r=0.0575; T=1; n=269; M=100;
%---Inisialisasi.
estimasi;
S=zeros(M,n);
S(:,1)=S0;
dt=T/n; % time-step
t=(0:dt:n*dt); % vektor titik waktu
%---Harga-harga aset pada setiap simulasi.
randn('state',100);
for m=1:M
for i=1:n
S(m,i+1)=S(m,i)*exp((r-0.5*sigma_MLE^2)*dt+(sigma_MLE*sqrt(dt))*randn);
end
figure(1)
plot(t,S(m,:),'-'), hold on
end
hold off
xlabel('waktu'), ylabel('Harga Saham')
title('Simulasi Pergerakan Harga Saham')
figure(2)
plot(1:M,S(:,n+1),'-')
xlabel('simulasi'), ylabel('Harga Saham')
title('Simulasi Harga Saham Saat Satu Tahun Kedepan')
6
Algoritma Matlab untuk menentukan harga opsi adalah sebagai berikut:
St=S(:,n+1);
%Nilai Opsi Call Eropa
K = [50000 53000 56000];
for i = 1:3
C(i)=(sum(exp(-r*T)*max(0,St-K(i))))./M;
end
%Nilai Opsi Call Eropa
for i = 1:3
P(i)=(sum(exp(-r*T)*max(0,K(i)-St)))./M;
end
[K' C' P']
Algoritma Matlab untuk simulasi pergerakan harga saham tiga bulan kedepan serta
mendapatkan nilai prosentase nilai error yang maksimum adalah sebagai berikut:
clc
clear all
%---Parameter-parameter metode.
S0=53000; T=1/4; n=61; M=100;
%---Inisialisasi.
estimasi;
S=zeros(M,n);
galat=zeros(1,n);
S(:,1)=S0;
dt=T/n; % time-step
t=(0:dt:n*dt); % vektor titik waktu
%---Harga-harga aset pada setiap simulasi.
randn('state',100);
for m=1:M
for i=1:n
S(m,i+1)=S(m,i)*exp((myu_MLE-0.5*sigma_MLE^2)*dt+(sigma_MLE*sqrt(dt))*randn);
end
figure(1)
plot(t,S(m,:),'-'), hold on
end
hold off
xlabel('waktu(Tahun)'), ylabel('Harga Saham(Rupiah)')
title('Simulasi Pergerakan Harga Saham')
%studi error dari simulasi
data2=csvread('HMSP2.csv')';
galat=(abs((mean(S))'-data2')./data2')*100;
max(galat)
7
figure(2)
plot(data2)
xlabel('waktu(Hari)'), ylabel('Harga Saham')
title('Harga Saham PT. HM Sampoerna Tbk. tanggal 29 Februari sampai 31 Mei 2012')
figure(3)
plot(galat)
xlabel('waktu(Hari)'), ylabel('Error Dari Simulasi (dalam persen)')
title('Studi Error')
8