A novel reconstruction method from contours lines is provided. First, we use a simple method to get rid of redundant points on every contour, then we interpolate them by using cubic Bézier spline curve. For corre...A novel reconstruction method from contours lines is provided. First, we use a simple method to get rid of redundant points on every contour, then we interpolate them by using cubic Bézier spline curve. For corresponding points of different con- tours, we interpolate them by the cubic Bézier spline curve too, so the whole surface can be reconstructed by the bi-cubic Bézier spline surface. The reconstructed surface is smooth because every Bézier surface is patched with G2 continuity, the reconstruction speed is fast because we can use the forward elimination and backward substitution method to solve the system of tridiagonal equations. We give some reconstruction examples at the end of this paper. Experiments showed that our method is applicable and effective.展开更多
This paper studies the traditional local volatility model and proposes:A novel local volatility model with mean-reversion process.The larger is the gap between local volatility and its mean level,the higher will be th...This paper studies the traditional local volatility model and proposes:A novel local volatility model with mean-reversion process.The larger is the gap between local volatility and its mean level,the higher will be the rate at which local volatility will revert to the mean.Then,a B-spline method with proper knot control is applied to interpolate the local volatility matrix.The bi-cubic B-spline is used to recover the local volatility surface from this local volatility matrix.Finally,empirical tests show that the proposed mean-reversion local volatility model offers better prediction performance than the traditional local volatility model.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 60373070 and 60573147), Postdoctor Foundation of Shanghai (No. 05R214129), and Zhejiang Education Foundation of China (No. 20050786)
文摘A novel reconstruction method from contours lines is provided. First, we use a simple method to get rid of redundant points on every contour, then we interpolate them by using cubic Bézier spline curve. For corresponding points of different con- tours, we interpolate them by the cubic Bézier spline curve too, so the whole surface can be reconstructed by the bi-cubic Bézier spline surface. The reconstructed surface is smooth because every Bézier surface is patched with G2 continuity, the reconstruction speed is fast because we can use the forward elimination and backward substitution method to solve the system of tridiagonal equations. We give some reconstruction examples at the end of this paper. Experiments showed that our method is applicable and effective.
文摘This paper studies the traditional local volatility model and proposes:A novel local volatility model with mean-reversion process.The larger is the gap between local volatility and its mean level,the higher will be the rate at which local volatility will revert to the mean.Then,a B-spline method with proper knot control is applied to interpolate the local volatility matrix.The bi-cubic B-spline is used to recover the local volatility surface from this local volatility matrix.Finally,empirical tests show that the proposed mean-reversion local volatility model offers better prediction performance than the traditional local volatility model.
