49,943 research outputs found
B-spline techniques for volatility modeling
This paper is devoted to the application of B-splines to volatility modeling,
specifically the calibration of the leverage function in stochastic local
volatility models and the parameterization of an arbitrage-free implied
volatility surface calibrated to sparse option data. We use an extension of
classical B-splines obtained by including basis functions with infinite
support. We first come back to the application of shape-constrained B-splines
to the estimation of conditional expectations, not merely from a scatter plot
but also from the given marginal distributions. An application is the Monte
Carlo calibration of stochastic local volatility models by Markov projection.
Then we present a new technique for the calibration of an implied volatility
surface to sparse option data. We use a B-spline parameterization of the
Radon-Nikodym derivative of the underlying's risk-neutral probability density
with respect to a roughly calibrated base model. We show that this method
provides smooth arbitrage-free implied volatility surfaces. Finally, we sketch
a Galerkin method with B-spline finite elements to the solution of the partial
differential equation satisfied by the Radon-Nikodym derivative.Comment: 25 page
Statistical applications of the multivariate skew-normal distribution
Azzalini & Dalla Valle (1996) have recently discussed the multivariate
skew-normal distribution which extends the class of normal distributions by the
addition of a shape parameter. The first part of the present paper examines
further probabilistic properties of the distribution, with special emphasis on
aspects of statistical relevance. Inferential and other statistical issues are
discussed in the following part, with applications to some multivariate
statistics problems, illustrated by numerical examples. Finally, a further
extension is described which introduces a skewing factor of an elliptical
density.Comment: full-length version of the published paper, 32 pages, with 7 figures,
uses psfra
Distributions generated by perturbation of symmetry with emphasis on a multivariate skew distribution
A fairly general procedure is studied to perturbate a multivariate density
satisfying a weak form of multivariate symmetry, and to generate a whole set of
non-symmetric densities. The approach is general enough to encompass a number
of recent proposals in the literature, variously related to the skew normal
distribution. The special case of skew elliptical densities is examined in
detail, establishing connections with existing similar work. The final part of
the paper specializes further to a form of multivariate skew density.
Likelihood inference for this distribution is examined, and it is illustrated
with numerical examples.Comment: full-length version of the published paper, 31 pages with 9 figure
Computationally efficient recursions for top-order invariant polynomials with applications
The top-order zonal polynomials Ck(A),and top-order invariant polynomials Ck1,...,kr(A1,...,Ar)in which each of the partitions of ki,i = 1,..., r,has only one part, occur frequently in multivariate distribution theory, and econometrics - see, for example Phillips (1980, 1984, 1985, 1986), Hillier (1985, 2001), Hillier and Satchell (1986), and Smith (1989, 1993). However, even with the recursive algorithms of Ruben (1962) and Chikuse (1987), numerical evaluation of these invariant polynomials is extremely time consuming. As a result, the value of invariant polynomials has been largely confined to analytic work on distribution theory. In this paper we present new, very much more efficient, algorithms for computing both the top-order zonal and invariant polynomials. These results should make the theoretical results involving these functions much more valuable for direct practical study. We demonstrate the value of our results by providing fast and accurate algorithms for computing the moments of a ratio of quadratic forms in normal random variables.
On the distribution of estimators of diffusion constants for Brownian motion
We discuss the distribution of various estimators for extracting the
diffusion constant of single Brownian trajectories obtained by fitting the
squared displacement of the trajectory. The analysis of the problem can be
framed in terms of quadratic functionals of Brownian motion that correspond to
the Euclidean path integral for simple Harmonic oscillators with time dependent
frequencies. Explicit analytical results are given for the distribution of the
diffusion constant estimator in a number of cases and our results are confirmed
by numerical simulations.Comment: 14 pages, 5 figure
Some Historical Aspects of Error Calculus by Dirichlet Forms
We discuss the main stages of development of the error calculation since the
beginning of XIX-th century by insisting on what prefigures the use of
Dirichlet forms and emphasizing the mathematical properties that make the use
of Dirichlet forms more relevant and efficient. The purpose of the paper is
mainly to clarify the concepts. We also indicate some possible future research.Comment: 18 page
Bayesian analysis of DSGE models
This paper reviews Bayesian methods that have been developed in recent years to estimate and evaluate dynamic stochastic general equilibrium (DSGE) models. We consider the estimation of linearized DSGE models, the evaluation of models based on Bayesian model checking, posterior odds comparisons, and comparisons to vector autoregressions, as well as the nonlinear estimation based on a second-order accurate model solution. These methods are applied to data generated from correctly specified and misspecified linearized DSGE models, and a DSGE model that was solved with a second-order perturbation method.Macroeconomics ; Vector autoregression
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