#TITLE_ALTERNATIVE#
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 gen...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/17792 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Brownian motion assumption is popular used in …nancial mathematics modelling, but brownian motion could not theoritically capture jumps phenomenons in real <br />
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…nancial data. Many literatures said Levy Process is extremely fashionable with nancial data because by generalizing the brownian motion into Levy process allow <br />
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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 />
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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 />
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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 />
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the general stochastic process. Inverse Gaussian process is choosen to represent the subordinator Euler discritization scheme is popular method to simulate the <br />
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Ornstein-Uhlenbeck process with estimated parameters by method of moments. |
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