Perbandingan metode monte carlo dan quasi monte carlo dalam menghitung opsi Asia = Comprehensive comparison of monte carlo simulation and quasi monte carlo simulation for pricing Asian options

Ekanugraha, Zefanya Aditya Sabat (2024) Perbandingan metode monte carlo dan quasi monte carlo dalam menghitung opsi Asia = Comprehensive comparison of monte carlo simulation and quasi monte carlo simulation for pricing Asian options. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Investasi merupakan aktivitas krusial untuk untuk semua orang. Berbagai instrumen tersedia untuk memenuhi tingkat risiko konsumen. Masa kini, tersedia berbagai produk derivatif, diantaranya futures, swaps, dan options. Dalam berinvestasi opsi, perlu diperhatikan harga, baik untuk posisi put atau call. Opsi eksotis adalah salah satu pilihan yang tersedia untuk lindung nilai. Opsi Asia adalah opsi eksotis yang unik karena valuasinya lebih murah daripada opsi lainnya dan memiliki sifat path dependency. Sifat unik ini menimbulkan tantangan dalam menentukan harga opsi. Berbagai penelitian terdahulu mencoba menangani masalah ini yaitu dengan pendekatan persamaan diferensial parsial, simulasi Quasi-Monte Carlo, dan metode binomial. Penelitian ini bertujuan untuk mengetahui manakah metode yang terbaik antara Monte Carlo standar dan Quasi-Monte Carlo dan seberapa signifikan. Perbandingan meliputi Monte Carlo standar menggunakan bilangan normal standar, Quasi-Monte Carlo menggunakan bilangan Halton, dan Quasi-Monte Carlo menggunakan bilangan Sobol. Melalui uji beda, didapatkan hasil penelitian bahwa simulasi Quasi-Monte Carlo menggunakan bilangan Sobol secara signikan merupakan simulasi yang paling superior dibandingkan simulasi Quasi-Monte Carlo menggunakan bilangan Halton dan simulasi Monte Carlo menggunakan bilangan normal standar. / Investment is a crucial activity for everyone. Various instruments are available to meet consumers’ risk levels. Currently, there are various derivative products available, including futures, swaps, and options. When investing in options, it is important to compute the price, both for put or call positions. Exotic options are one of the choices available for hedging. Asian options are exotic options that are unique because their valuation is cheaper than other options and they have path dependency properties. These unique properties pose challenges in determining option prices. Various previous studies have attempted to address this issue using approaches such as partial differential equation methods, Quasi-Monte Carlo simulations, and binomial methods. This study aims to determine which method is best between standard Monte Carlo and Quasi-Monte Carlo and how significant the difference is. Comparison comprises of standard Monte Carlo using normally distributed sequence, Quasi-Monte Carlo using Halton sequence, and Quasi-Monte Carlo using Sobol sequence. Through nonparametric difference test, the research findings indicate that quasi-random numbers, specifically Sobol numbers, significantly outperform Halton and standard normal numbers.

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