#TITLE_ALTERNATIVE#

• Main Author: PUTRA UTAMA (NIM : 10109067); Pembimbing : Dr. Muhammad Syamsuddin, M.Com , ADITYA
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/17792
• Institution: Institut Teknologi Bandung

Brownian motion assumption is popular used in …nancial mathematics modelling, but brownian motion could not theoritically capture jumps phenomenons in real <br /> <br /> …nancial data. Many literatures said Levy Process is extremely fashionable with nancial data because by generalizing the brownian motion into Levy process allow <br /> <br /> <br /> <br /> <br /> <br /> us to capture jumps. Besides, some real …nancial datas, such as interest rate and exchange rate, have mean-reverting property. One of common process to model <br /> <br /> <br /> <br /> <br /> <br /> the mean-reverting data is Ornstein-Uhlenbeck process, but Its value could be negative. In fact, the interest rate and exchange rate could not be negative. The <br /> <br /> <br /> <br /> <br /> <br /> Ornstein-Uhlenbeck process also could not capture jumps phenomenons. Lacks of Ornstein-Uhlenbeck process is covered if the brownian motion as the basic of Ornstein-Uhlenbeck process change into subordinator Levy process, <br /> <br /> <br /> <br /> <br /> <br /> the general stochastic process. Inverse Gaussian process is choosen to represent the subordinator Euler discritization scheme is popular method to simulate the <br /> <br /> <br /> <br /> <br /> <br /> Ornstein-Uhlenbeck process with estimated parameters by method of moments.