LEMBAR PENGESAHAN LEMBAR PERNYATAAN ABSTRAK KATA PENGANTAR UCAPAN TERIMA KASIH DAFTAR ISI DAFTAR TABEL DAFTAR GAMBAR DAFTAR LAMPIRAN

DAFTAR ISI

Halaman LEMBAR PENGESAHAN LEMBAR PERNYATAAN ABSTRAK .......................................................................................................... i KATA PENGANTAR ........................................................................................ iii UCAPAN TERIMA KASIH ............................................................................. iv DAFTAR ISI ....................................................................................................... v DAFTAR TABEL .............................................................................................. vii DAFTAR GAMBAR .......................................................................................... viii DAFTAR LAMPIRAN ...................................................................................... x

BAB I PENDAHULUAN ................................................................................... 1 1.1

Latar Belakang ............................................................................................ 1

1.2

Rumusan Masalah ....................................................................................... 3

1.3

Tujuan Penulisan ........................................................................................ 4

1.4

Batasan Masalah ......................................................................................... 4

1.5

Manfaat Penulisan ...................................................................................... 4

1.6

Sistematika Penulisan ................................................................................. 5

BAB II KAJIAN PUSTAKA ............................................................................. 6 2.1

Pasar Modal ................................................................................................ 6

2.2

Saham ......................................................................................................... 6

2.3

Variabel Acak dan Proses Stokastik ........................................................... 8

2.4

Proses Markov dan Proses Stokastik dengan Waktu Kontinu .................... 9

2.5

Model Harga Saham ................................................................................... 13

2.6

Opsi ............................................................................................................. 18

2.7

Opsi Eropa .................................................................................................. 20

2.8

Model Black-Scholes-Merton ..................................................................... 23

FIKA DARA NURINA FIRDAUS, 2013 Aplikasi Metode Monte Carlo Pada Penentuan harga Opsi Eropa Universitas Pendidikan Indonesia | repository.upi.edu

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v

2.9

Strong Law of Large Number dan Teorema Limit Pusat ............................ 27 Halaman

BAB III METODE MONTE CARLO ............................................................... 29 3.1

Metode Monte Carlo ................................................................................... 29

3.2

Pemodelan Harga Saham untuk Metode Monte Carlo ............................... 29

3.3

Penentuan Harga Opsi Eropa dengan Metode Monte Carlo ...................... 33

3.4

Rekursif Backward ..................................................................................... 33

3.5

Algoritma Penentuan Harga Opsi Eropa dengan Metode Monte Carlo ..... 36

BAB IV HASIL NUMERIK PENENTUAN HARGA OPSI EROPA MENGGUNAKAN METODE MONTE CARLO ............................... 38 4.1

Penentuan Harga Opsi Eropa Menggunakan Metode Monte Carlo ........... 39

4.2

Pengaruh Parameter-Parameter pada Metode Monte Carlo dalam Menentukan Harga Opsi Eropa ........................................................ 42

4.3

Kecepatan dan Keakuratan Metode Monte Carlo dalam Menentukan Harga Opsi Eropa ........................................................ 58

BAB V PENUTUP .............................................................................................. 66 5.1

Kesimpulan ................................................................................................. 66

5.2

Saran ........................................................................................................... 67

DAFTAR PUSTAKA ......................................................................................... 68 LAMPIRAN ........................................................................................................ 70 RIWAYAT HIDUP ............................................................................................ 134

FIKA DARA NURINA FIRDAUS, 2013 Aplikasi Metode Monte Carlo Pada Penentuan harga Opsi Eropa Universitas Pendidikan Indonesia | repository.upi.edu

DAFTAR TABEL

Tabel

Halaman

4.1. Pengaruh Harga Saham Awal terhadap Harga Opsi Call Eropa ................ 43 4.2. Pengaruh Harga Saham Awal terhadap Harga Opsi Put Eropa .................. 44 4.3. Pengaruh Strike Price terhadap Harga Opsi Call Eropa ............................. 46 4.4. Pengaruh Strike Price terhadap Harga Opsi Put Eropa .............................. 48 4.5. Pengaruh Waktu Jatuh Tempo terhadap Harga Opsi Call Eropa ............... 49 4.6. Pengaruh Waktu Jatuh Tempo terhadap Harga Opsi Put Eropa ................. 51 4.7. Pengaruh Volatilitas terhadap Harga Opsi Call Eropa ............................... 52 4.8. Pengaruh Volatilitas terhadap Harga Opsi Put Eropa ................................ 54 4.9. Pengaruh Tingkat Suku Bunga terhadap Harga Opsi Call Eropa ............... 55 4.10. Pengaruh Tingkat Suku Bunga terhadap Harga Opsi Put Eropa ................ 57 4.11. Pengaruh Jumlah Partisi Waktu terhadap Harga Opsi Call Eropa ............. 59 4.12. Pengaruh Jumlah Partisi Waktu terhadap Harga Opsi Put Eropa ............... 61

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DAFTAR GAMBAR

Gambar

Halaman

2.1. Ilustrasi Definisi Variabel Acak ................................................................. 8 2.2. Diagram Fungsi Payoff dari Opsi Call Eropa dengan Strike Price 𝐾 ........ 21 2.3. Diagram Fungsi Payoff dari Opsi Put Eropa dengan Strike Price 𝐾 .......... 23 3.1. Ilustrasi Penentuan Harga Saham Saat 𝑇 Berdasarkan Harga Saham Sebelumnya ................................................................................................. 32 3.2. Ilustrasi Penentuan Harga Saham Saat Partisi-Partisi Waktu Berdasarkan Harga Saham Awal ..................................................................................... 32 3.3. Ilustrasi Rekursif Backward ....................................................................... 34 3.4. Flow Chart Algoritma Metode Monte Carlo .............................................. 37 4.1. Kemungkinan Pergerakan Harga Saham untuk Opsi Call Eropa ............... 39 4.2. Kemungkinan Pergerakan Harga Saham untuk Opsi Put Eropa ................ 40 4.3. Grafik Pengaruh Harga Saham Awal terhadap Harga Opsi Call Eropa ..... 44 4.4. Grafik Pengaruh Harga Saham Awal terhadap Harga Opsi Put Eropa ...... 46 4.5. Grafik Pengaruh Strike Price terhadap Harga Opsi Call Eropa ................. 47 4.6. Grafik Pengaruh Strike Price terhadap Harga Opsi Put Eropa ................... 49 4.7. Grafik Pengaruh Waktu Jatuh Tempo terhadap Harga Opsi Call Eropa ................................................................................ 50 4.8. Grafik Pengaruh Waktu Jatuh Tempo terhadap Harga Opsi Put Eropa ................................................................................. 52 4.9. Grafik Pengaruh Volatilitas terhadap Harga Opsi Call Eropa .................... 53 4.10. Grafik Pengaruh Volatilitas terhadap Harga Opsi Put Eropa ..................... 55 4.11. Grafik Pengaruh Tingkat Suku Bunga terhadap Harga Opsi Call Eropa ................................................................................ 56 4.12. Grafik Pengaruh Tingkat Suku Bunga terhadap Harga Opsi Put Eropa ................................................................................. 58 4.13. Grafik Pengaruh Jumlah Partisi Waktu terhadap Harga Opsi Call Eropa ................................................................................ 61 4.14. Grafik Pengaruh Jumlah Partisi Waktu terhadap Harga Opsi Put Eropa ................................................................................. 63 FIKA DARA NURINA FIRDAUS, 2013 Aplikasi Metode Monte Carlo Pada Penentuan harga Opsi Eropa Universitas Pendidikan Indonesia | repository.upi.edu

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Gambar

Halaman

4.15. Grafik Perubahan Nilai Error pada Penentuan Harga Opsi Call Eropa ..... 64 4.16. Grafik Perubahan Nilai Error pada Penentuan Harga Opsi Put Eropa ...... 65

DAFTAR LAMPIRAN

Lampiran A

Halaman

..................................................................................................................... 71 A.1 Distribusi dari ∆𝑧 .............................................................................. 71 A.2 Distribusi dari 𝑧(𝑇) − 𝑧(0) ............................................................... 71 A.3 Proses Pengintegralan 𝑑𝑥 = 𝑎. 𝑑𝑡 ..................................................... 72 A.4 Distribusi dari ∆𝑥 .............................................................................. 73 A.5 Distribusi dari 𝑥 𝑇 − 𝑥(0) .............................................................. 73

B

..................................................................................................................... 76 B.1 Penentuan Distribusi dari

∆𝑆 𝑆

.............................................................. 76

B.2 Pembuktian Lemma Itô ..................................................................... 76 B.3 Penentuan Distribusi dari ln 𝑆𝑇 − ln 𝑆0 ....................................... 79 B.4 Penentuan Rata-Rata dan Varians dari 𝑆𝑇 ......................................... 81 C

..................................................................................................................... 84 C.1 Persamaan Diferensial Black-Scholes-Merton .................................. 84 C.2 Perumusan Harga Opsi Call Eropa dan Opsi Put Eropa ................... 85

D

..................................................................................................................... 91 D.1 Pembuktian Strong Law of Large Numbers ...................................... 91 D.2 Pembuktian Teorema Limit Pusat ..................................................... 93

E

..................................................................................................................... 96 E.1 Ilustrasi Kontruksi Jalur Pergerakan Harga Saham ........................... 96 E.2 Perhitungan Simpangan Baku untuk Opsi Eropa .............................. 97

F

..................................................................................................................... 99 F.1

Program Penentuan Harga Opsi Call Eropa ...................................... 99

F.2

Program Penentuan Harga Opsi Put Eropa ....................................... 101

FIKA DARA NURINA FIRDAUS, 2013 Aplikasi Metode Monte Carlo Pada Penentuan harga Opsi Eropa Universitas Pendidikan Indonesia | repository.upi.edu

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Lampiran G

Halaman

..................................................................................................................... 103 G.1 Perhitungan Volatilitas Tahunan ....................................................... 103 G.2 Tabel Harga Saham Berdasarkan Harga Saham Awal untuk Opsi Call Eropa ....................................................................... 106 G.3 Tabel Penentuan Harga Saham Berdasarkan Harga Saham Awal untuk Opsi Put Eropa ........................................................................ 120