#TITLE_ALTERNATIVE# - PUTRA UTAMA (NIM : 10109067); Pembimbing : Dr. Muhammad Syamsuddin, M.Com , ADITYA
Brownian motion assumption is popular used in …nancial mathematics modelling, but brownian motion could not theoritically capture jumps phenomenons in real …nancial data. Many literatures said Levy Process is extremely fashionable with nancial data because by generalizing the brownian motion into Levy process allow 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 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 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, the general stochastic process. Inverse Gaussian process is choosen to represent the subordinator Euler discritization scheme is popular method to simulate the Ornstein-Uhlenbeck process with estimated parameters by method of moments.