#TITLE_ALTERNATIVE#
Brownian motion assumption is popular used in financial mathematics modelling, but brownian motion could not theoritically capture jumps phenomenons in real <br /> <br /> <br /> <br /> <br /> financial data. Many literatures said Levy Process is extremely fashiona...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/14657 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Brownian motion assumption is popular used in financial mathematics modelling, but brownian motion could not theoritically capture jumps phenomenons in real <br />
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financial data. Many literatures said Levy Process is extremely fashionable with financial data because by generalizing the brownian motion into Levy process allow <br />
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us to capture jumps. Besides, some real financial 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. |
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