The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
George Tauchen - One of the best experts on this subject based on the ideXlab platform.
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the realized Laplace Transform of volatility
Econometrica, 2012Co-Authors: Viktor Todorov, George TauchenAbstract:We introduce and derive the asymptotic behavior of a new measure constructed from high-frequency data which we call the realized Laplace Transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace Transform function of the latent stochastic volatility process over a given interval of time and is robust to the presence of jumps in the price process. With a long span of data, that is, under joint long-span and infill asymptotics, the statistic can be used to construct a nonparametric estimate of the volatility Laplace Transform as well as of the integrated joint Laplace Transform of volatility over different points of time. We derive feasible functional limit theorems for our statistic both under fixed-span and infill asymptotics as well as under joint long-span and infill asymptotics which allow us to quantify the precision in estimation under both sampling schemes.
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The Realized Laplace Transform of Volatility
Econometrica, 2012Co-Authors: Viktor Todorov, George TauchenAbstract:We introduce a new measure constructed from high-frequency financial data which we call the Realized Laplace Transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace Transform of the latent stochastic volatility process over a given interval of time. When a long span of data is used, i.e., under joint long-span and fill-in asymptotics, it is an estimate of the volatility Laplace Transform. The asymptotic behavior of the statistic depends on the small scale behavior of the driving martingale. We derive the asymptotics both in the case when the latter is known and when it needs to be inferred from the data. When the underlying process is a jump-diffusion our statistic is robust to jumps and when the process is pure-jump it is robust to presence of less active jumps. We apply our results to simulated and real financial data.
Yangquan Chen - One of the best experts on this subject based on the ideXlab platform.
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analytical calculation of the inverse nabla Laplace Transform
Chinese Control and Decision Conference, 2020Co-Authors: Yiheng Wei, Yuquan Chen, Yangquan Chen, Yong WangAbstract:The inversion of nabla Laplace Transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction expansion method are developed to perform the inverse nabla Laplace Transform. For the first method, two alternative formulae are proposed when adopting the poles inside or outside of the contour, respectively. For the second method, a table on the Transform pairs of those popular functions is carefully established. Besides illustrating the effectiveness of the developed methods with two illustrative examples, the applicability are further discussed in the fractional order case.
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analytical calculation of the inverse nabla Laplace Transform
arXiv: General Mathematics, 2019Co-Authors: Yuquan Chen, Yangquan ChenAbstract:The inversion of nabla Laplace Transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace Transform. For the first method, two alternative formulae are proposed when adopting the poles inside or outside of the contour, respectively. For the second method, a table on the Transform pairs of those popular functions is carefully established. Besides illustrating the effectiveness of the developed methods with two illustrative examples, the applicability are further discussed in the fractional order case.
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Application of numerical inverse Laplace Transform algorithms in fractional calculus
Journal of the Franklin Institute, 2011Co-Authors: Hu Sheng, Yangquan ChenAbstract:Laplace Transform technique has been considered as an efficient way in solving differential equations with integer-order. But for differential equations with non-integer order, the Laplace Transform technique works effectively only for relatively simple equations, because of the difficulties of calculating inversion of Laplace Transforms. Motivated by finding an easy way to numerically solve the complicated fractional-order differential equations, we investigate the validity of applying numerical inverse Laplace Transform algorithms in fractional calculus. Three numerical inverse Laplace Transform algorithms, named Invlap, Gavsteh and NILT, were tested using Laplace Transforms of fractional-order equations. Based on the comparison between analytical results and numerical inverse Laplace Transform algorithm results, the effectiveness and reliability of numerical inverse Laplace Transform algorithms for fractional-order differential equations was confirmed.
Viktor Todorov - One of the best experts on this subject based on the ideXlab platform.
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the realized Laplace Transform of volatility
Econometrica, 2012Co-Authors: Viktor Todorov, George TauchenAbstract:We introduce and derive the asymptotic behavior of a new measure constructed from high-frequency data which we call the realized Laplace Transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace Transform function of the latent stochastic volatility process over a given interval of time and is robust to the presence of jumps in the price process. With a long span of data, that is, under joint long-span and infill asymptotics, the statistic can be used to construct a nonparametric estimate of the volatility Laplace Transform as well as of the integrated joint Laplace Transform of volatility over different points of time. We derive feasible functional limit theorems for our statistic both under fixed-span and infill asymptotics as well as under joint long-span and infill asymptotics which allow us to quantify the precision in estimation under both sampling schemes.
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The Realized Laplace Transform of Volatility
Econometrica, 2012Co-Authors: Viktor Todorov, George TauchenAbstract:We introduce a new measure constructed from high-frequency financial data which we call the Realized Laplace Transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace Transform of the latent stochastic volatility process over a given interval of time. When a long span of data is used, i.e., under joint long-span and fill-in asymptotics, it is an estimate of the volatility Laplace Transform. The asymptotic behavior of the statistic depends on the small scale behavior of the driving martingale. We derive the asymptotics both in the case when the latter is known and when it needs to be inferred from the data. When the underlying process is a jump-diffusion our statistic is robust to jumps and when the process is pure-jump it is robust to presence of less active jumps. We apply our results to simulated and real financial data.
Abdulaziz Al-shuaibi - One of the best experts on this subject based on the ideXlab platform.
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The Inverse Laplace Transform and Analytic Pseudo-Differential Operators
Journal of Mathematical Analysis and Applications, 1998Co-Authors: Amin Boumenir, Abdulaziz Al-shuaibiAbstract:Abstract By comparing the Laplace Transform L with the differential operatorD, we obtain a formula for the inverse Laplace Transform L − 1 = (1/π)V − 1 cos(πD)V L , whereVis a unitary Transformation operator. This helps us obtain an explicit spectral representation of L . Some applications of the above relation are discussed.
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A regularization method for approximating the inverse Laplace Transform
Analysis in Theory and Applications, 1997Co-Authors: Abdulaziz Al-shuaibiAbstract:A new method for approximating the inerse Laplace Transform is presented. We first change our Laplace Transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier Transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace Transform as finite sum $$f\left( t \right) \cong \sum\limits_{b \approx 0}^N {b_k \left( \alpha \right)\frac{{d^h G\left( x \right)}} {{dx^h }}}$$ , where bk(a) are precalculated and tabulated regularization coefficients, G(x)=ex(ex) and g(x) is the given Laplace Transform of f(t). Error bounds together with an algorithm to calculate the coefficients bk (a) and some examples are also discussed. Perturbed data problems are not included.
Martino Grasselli - One of the best experts on this subject based on the ideXlab platform.
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the explicit Laplace Transform for the wishart process
Journal of Applied Probability, 2014Co-Authors: Alessandro Gnoatto, Martino GrasselliAbstract:We derive the explicit formula for the joint Laplace Transform of the Wishart process and its time integral, which extends the original approach of Bru (1991). We compare our methodology with the alternative results given by the variation-of-constants method, the linearization of the matrix Riccati ordinary differential equation, and the Runge-Kutta algorithm. The new formula turns out to be fast and accurate.
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the explicit Laplace Transform for the wishart process
Research Papers in Economics, 2013Co-Authors: Alessandro Gnoatto, Martino GrasselliAbstract:We derive the explicit formula for the joint Laplace Transform of the Wishart process and its time integral which extends the original approach of Bru. We compare our methodology with the alternative results given by the variation of constants method, the linearization of the Matrix Riccati ODE's and the Runge-Kutta algorithm. The new formula turns out to be fast and accurate.
