Metode Martingale dalam penentuan harga opsi Toe Eropa dengan menggunakan pendekatan Waktu Kontinu pada Pasar (B,S).

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METODE MARTINGALE DALAM PENENTUAN FIARGA OPSI TIPE EROPA DENGAN MENGGUNAKAN

PENDEKATAN WAKTU KONTINU PADA PASAR (B,S)

Chatarina Enny Murwaningtyas.

INTISARI

Dibawah bimbingan Prof. Drs. Suryo Guritno, M.Stats.,Ph.D1)

Tesis ini mempelajari tentang matematika finansial terutama tentang penentuan harga opsi tipe Eropa dengan pendekatan waktu kontinu. Diasumsikan suatu pasar (8,S) dijalankan pada waktu kontinu. Rekening bank yang tidak beresiko 13 = (B,),0 disusun menurut formula bunga majemuk, dan saham yang mempunyai resiko S = (St)po ditentukan oleh geometric Brownian motion.

Teori penentuan harga martingale disajikan pada harga opsi yang rasional, strategi hedging, dan waktu ekspirasi yang rasional. Formula Black-Scholes untuk opsi call tipe Eropa dihasilkan. Dalam tesis ini juga mempertimbangkan contoh tertentu opsi Eropa.

Kata kunci : sekuritas yang beresiko dan yang tidak beresiko, opsi, strategi hedging, geometric Brownian motion, opsi standar dan exotic, formula Black-Scholes, keseimbangan put-call, ukuran martingale.

1) Jurusan Matematika, FMIPA UGM.

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MARTINGALE METHODS ON THE THEORY OF

PRICING OF OPTIONS OF EUROPEAN TYPE WITH CONTINUOUSLY IN TIME ON (B,S)-MARKET

Chatarina Enny Murwaningtyas.

ABSTRACT

Under Supervision of Prof. Drs. Suryo Guritno, M.Stats.,Ph.DI)

This thesis study about financial mathematics, especially about the theory of pricing of options of European type with continuously in time. It is 'assumed that a (B,S) market is operating continuously in time. The riskless bank account B = (B0po is evolving according to the "compound interests" formula, and a risky stock price S = (St)po is governed by geometric Brownian Motion.

The "martingale" pricing theory is presented for rational option price, hedging strategies, and rational expiration times. The Black-Scholes formula for standard European call option is derived. This thesis consider a number of other particular examples of European option.

Key words : risky and riskless securities, options, hedging strategies, geometric Brownian motion, standard and exotic options, Black-Scholes formula, put-call parity, martingale measure.

1) Department of mathematics, FMIPA UGM.

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