10,772 research outputs found
Monte Carlo Greeks for financial products via approximative transition densities
In this paper we introduce efficient Monte Carlo estimators for the valuation
of high-dimensional derivatives and their sensitivities (''Greeks''). These
estimators are based on an analytical, usually approximative representation of
the underlying density. We study approximative densities obtained by the WKB
method. The results are applied in the context of a Libor market model.Comment: 24 page
Variational Analysis of Constrained M-Estimators
We propose a unified framework for establishing existence of nonparametric
M-estimators, computing the corresponding estimates, and proving their strong
consistency when the class of functions is exceptionally rich. In particular,
the framework addresses situations where the class of functions is complex
involving information and assumptions about shape, pointwise bounds, location
of modes, height at modes, location of level-sets, values of moments, size of
subgradients, continuity, distance to a "prior" function, multivariate total
positivity, and any combination of the above. The class might be engineered to
perform well in a specific setting even in the presence of little data. The
framework views the class of functions as a subset of a particular metric space
of upper semicontinuous functions under the Attouch-Wets distance. In addition
to allowing a systematic treatment of numerous M-estimators, the framework
yields consistency of plug-in estimators of modes of densities, maximizers of
regression functions, level-sets of classifiers, and related quantities, and
also enables computation by means of approximating parametric classes. We
establish consistency through a one-sided law of large numbers, here extended
to sieves, that relaxes assumptions of uniform laws, while ensuring global
approximations even under model misspecification
An Extended Empirical Saddlepoint Approximation for Intractable Likelihoods
The challenges posed by complex stochastic models used in computational
ecology, biology and genetics have stimulated the development of approximate
approaches to statistical inference. Here we focus on Synthetic Likelihood
(SL), a procedure that reduces the observed and simulated data to a set of
summary statistics, and quantifies the discrepancy between them through a
synthetic likelihood function. SL requires little tuning, but it relies on the
approximate normality of the summary statistics. We relax this assumption by
proposing a novel, more flexible, density estimator: the Extended Empirical
Saddlepoint approximation. In addition to proving the consistency of SL, under
either the new or the Gaussian density estimator, we illustrate the method
using two examples. One of these is a complex individual-based forest model for
which SL offers one of the few practical possibilities for statistical
inference. The examples show that the new density estimator is able to capture
large departures from normality, while being scalable to high dimensions, and
this in turn leads to more accurate parameter estimates, relative to the
Gaussian alternative. The new density estimator is implemented by the esaddle R
package, which can be found on the Comprehensive R Archive Network (CRAN)
Online Sequential Monte Carlo smoother for partially observed stochastic differential equations
This paper introduces a new algorithm to approximate smoothed additive
functionals for partially observed stochastic differential equations. This
method relies on a recent procedure which allows to compute such approximations
online, i.e. as the observations are received, and with a computational
complexity growing linearly with the number of Monte Carlo samples. This online
smoother cannot be used directly in the case of partially observed stochastic
differential equations since the transition density of the latent data is
usually unknown. We prove that a similar algorithm may still be defined for
partially observed continuous processes by replacing this unknown quantity by
an unbiased estimator obtained for instance using general Poisson estimators.
We prove that this estimator is consistent and its performance are illustrated
using data from two models
A selective overview of nonparametric methods in financial econometrics
This paper gives a brief overview on the nonparametric techniques that are
useful for financial econometric problems. The problems include estimation and
inferences of instantaneous returns and volatility functions of
time-homogeneous and time-dependent diffusion processes, and estimation of
transition densities and state price densities. We first briefly describe the
problems and then outline main techniques and main results. Some useful
probabilistic aspects of diffusion processes are also briefly summarized to
facilitate our presentation and applications.Comment: 32 pages include 7 figure
Estimation of latent variable models for ordinal data via fully exponential Laplace approximation
Latent variable models for ordinal data represent a useful tool in different
fields of research in which the constructs of interest are not directly
observable. In such models, problems related to the integration of the
likelihood function can arise since analytical solutions do not exist.
Numerical approximations, like the widely used Gauss Hermite (GH) quadrature,
are generally applied to solve these problems. However, GH becomes unfeasible
as the number of latent variables increases. Thus, alternative solutions have
to be found. In this paper, we propose an extended version of the Laplace
method for approximating the integrals, known as fully exponential Laplace
approximation. It is computational feasible also in presence of many latent
variables, and it is more accurate than the classical Laplace method
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