| Parametric estimation of discretely sampled Gamma-OU processes |
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| 作者姓名： | ZHANG Shibin ZHANG Xinsheng & SUN Shuguang School of Management Fudan University Shanghai China |
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| 作者单位： | ZHANG Shibin，ZHANG Xinsheng & SUN Shuguang School of Management，Fudan University，Shanghai 200433，China; Department of Mathematics，Shanghai Maritime University，Shanghai 200135，China |
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| 摘 要： | The stationary Gamma-OU processes are recommended to be the volatility of the financial assets. A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper. The estimator of an intensity parameter A and its convergence result are given, and the simulations show that the estimation is quite accurate. Assuming that the parameter A is estimated, the maximum likelihood estimation of shape parameter c and scale parameter a, whose likelihood function is not explicitly computable, is considered. By means of the Gaver-Stehfest algorithm, we construct an explicit sequence of approximations to the likelihood function and show that it converges the true (but unkown) one. Maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and the approximation shares the asymptotic properties of the true maximum likelihood estimator. Some simulation experiments reveal that this method is still quite accurate in most of rational situations for the background of volatility.
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| 关 键 词： | Lévy process Lévy density |
| 收稿时间： | 14 March 2006 |
| 修稿时间： | 15 May 2006 |
Parametric estimation of discretely sampled Gamma-OU processes |
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| ZHANG Shibin,ZHANG Xinsheng & SUN Shuguang School of Management,Fudan University,Shanghai ,China,.Parametric estimation of discretely sampled Gamma-OU processes[J].Science in China(Mathematics),2006,49(9):1231-1257. |
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| Authors: | ZHANG Shibin ZHANG Xinsheng SUN Shuguang |
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| Institution: | 1. School of Management, Fudan University, Shanghai 200433, China;Department of Mathematics, Shanghai Maritime University, Shanghai 200135, China
2. School of Management, Fudan University, Shanghai 200433, China |
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| Abstract: | The stationary Gamma-OU processes are recommended to be the volatility of the financial assets. A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper. The estimator of an intensity parameter A and its convergence result are given, and the simulations show that the estimation is quite accurate. Assuming that the parameter A is estimated, the maximum likelihood estimation of shape parameter c and scale parameter a, whose likelihood function is not explicitly computable, is considered. By means of the Gaver-Stehfest algorithm, we construct an explicit sequence of approximations to the likelihood function and show that it converges the true (but unkown) one. Maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and the approximation shares the asymptotic properties of the true maximum likelihood estimator. Some simulation experiments reveal that this method is still quite accurate in most of rational situations for the background of volatility. |
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| Keywords: | Gamma-OU process transition function stochalihood estimation |
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