Abstract
Barrier option is an option where the payoff price depends on whether or not the stock price passes the barrier during its life time. The aim of the research is to compare the convergence between conditional Monte Carlo and antithetic variate methods in determining the call barrier option price. The call barrier option price is influenced by several factors: initial stock price, stock volatility, risk-free interest rate, maturity, strike price and barrier. The calculation of call barrier option price is obtained by simulating stock price movements with different simulation number. Based on the simulation result, it is obtained that the calculation of call barrier option price with conditional Monte Carlo method converge faster than the antithetic variate method.
Highlights
the stock price passes the barrier during its life time
The aim of the research is to compare the convergence between conditional Monte Carlo
The call barrier option price is influenced by several factors
Summary
Opsi merupakan suatu kontrak antara pihak penerbit opsi (writer) dan pihak pemegang opsi (holder) yang memberikan hak, bukan kewajiban kepada holder untuk membeli atau menjual aset pokok dengan suatu harga tertentu (strike price) pada saat tertentu di masa yang akan datang (expiration date). Pada penelitian Wang & Wang (2011), harga opsi put tipe barrier down and out dihitung menggunakan metode Monte Carlo standar dan variance reduction. Hasil penelitian ini menunjukkan bahwa penentuan harga opsi put tipe barrier down and out menggunakan metode control variate dan antithetic variate menghasilkan standard error yang lebih kecil dibandingkan metode conditional Monte Carlo dan kombinasi conditional Monte Carlo dengan importance sampling. Sehubungan dengan hasil penelitian Wang & Wang (2011), serta mengingat conditional Monte Carlo dan antithetic variate merupakan bagian dari Monte Carlo variance reduction yang konvergensinya cepat maka penulis tertarik untuk membandingkan kekonvergenan dari metode conditional Monte Carlo dan antithetic variate dalam menentukan harga opsi call tipe barrier down and out. Perhitungan harga opsi menggunakan metode antithetic variates mengikuti gerak Brown geometrik dengan cara membangkitkan dua bilangan acak yang berdistribusi normal standar dan dilanjutkan dengan menentukan nilai duga dan nilai duga antithetic yaitu:. Selanjutnya menghitung harga opsi call tipe barrier down and out untuk masing masing nilai duga dengan persamaan berikut:
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