17,542 research outputs found
Estimation with Numerical Integration on Sparse Grids
For the estimation of many econometric models, integrals without analytical solutions have to be evaluated. Examples include limited dependent variables and nonlinear panel data models. In the case of one-dimensional integrals, Gaussian quadrature is known to work efficiently for a large class of problems. In higher dimensions, similar approaches discussed in the literature are either very specific and hard to implement or suffer from exponentially rising computational costs in the number of dimensions - a problem known as the "curse of dimensionality" of numerical integration. We propose a strategy that shares the advantages of Gaussian quadrature methods, is very general and easily implemented, and does not suffer from the curse of dimensionality. Monte Carlo experiments for the random parameters logit model indicate the superior performance of the proposed method over simulation techniques
Estimation with Numerical Integration on Sparse Grids
For the estimation of many econometric models, integrals without analytical solutions have to be evaluated. Examples include limited dependent variables and nonlinear panel data models. In the case of one-dimensional integrals, Gaussian quadrature is known to work efficiently for a large class of problems. In higher dimensions, similar approaches discussed in the literature are either very specific and hard to implement or suffer from exponentially rising computational costs in the number of dimensions - a problem known as the "curse of dimensionality" of numerical integration. We propose a strategy that shares the advantages of Gaussian quadrature methods, is very general and easily implemented, and does not suffer from the curse of dimensionality. Monte Carlo experiments for the random parameters logit model indicate the superior performance of the proposed method over simulation techniques.Estimation; Quadrature; Simulation; Mixed Logit
Smoothing the payoff for efficient computation of Basket option prices
We consider the problem of pricing basket options in a multivariate Black
Scholes or Variance Gamma model. From a numerical point of view, pricing such
options corresponds to moderate and high dimensional numerical integration
problems with non-smooth integrands. Due to this lack of regularity, higher
order numerical integration techniques may not be directly available, requiring
the use of methods like Monte Carlo specifically designed to work for
non-regular problems. We propose to use the inherent smoothing property of the
density of the underlying in the above models to mollify the payoff function by
means of an exact conditional expectation. The resulting conditional
expectation is unbiased and yields a smooth integrand, which is amenable to the
efficient use of adaptive sparse grid cubature. Numerical examples indicate
that the high-order method may perform orders of magnitude faster compared to
Monte Carlo or Quasi Monte Carlo in dimensions up to 35
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