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In this paper I use Monte Carlo simulated option data to investigated the empirical power of six Risk Neutral Density (RND) estimation techniques. Three alternative approaches are used for comparison and the choice of the most suitable method depends on: their performance to correctly price options, their capacity to fit the true density - which is estimated from the undrelying assets series - and their ability to forecast the future realization of the underlying asset. I found that the decision depends on the purpose of the framework: for pricing purpose, the interpolation techniques would be adequate. However, if the aim is to extract market expectations, the Edge worth expansion should be used. [ABSTRACT FROM AUTHOR]

The objective of this paper is to study how algorithms of optimization affect the parametersestimation of Autoregressive AR(1)Models. In our research we have represented the AR(1) models in linear state space form and applied the Kalman Filters to estimate the different unknown parameters of the model. Many methods have been proposed by researchers for the estimation of the parameters in the case of the linear state space models. In our work we have emphasized on the estimation through the Maximum Likelihood (ML). Statisticians have used many algorithms to optimise the likelihood function and they have proposed many filters; publishing their results in many papers. In spite of the fact that this field is so extended, we have emphasized our study in the financial field. Two quasi-Newton algorithms: Berndt, Hall, Hall, and Hausman (BHHH) and Broyden-Fletcher-Goldfarb-Shanno (BFGS), and the Expectation-Maximization (EM) algorithm have been chosen for this study. A practical study of these algorithms applied to the maximization of likelihood by means of the Kalman Filter have been done. The results are focused on efficiency in time of computation and precision of the unknown parameters estimation. A simulation study has been carried out, using as true values the parameters of this model published in the literature, in order to test the efficiency and precision of our implemented algorithms. [ABSTRACT FROM AUTHOR]

In This paper we propose a simple and easy-to-use method for computing accurate estimate (in closed form) of the double barrier hitting time distribution of a mean-reverting lognormal process, and discuss its application to pricing exotic options whose payoffs are contingent upon barrier hitting times. This new approach is also to provide tight upper and lower bounds (in closed form) of the exact result. Within the multi-stage approximation scheme, the estimate and bounds can be easily improved in a systematic manner. Furthermore, this approach can be straight-forwardly extended to those cases with specified moving boundaries as well. [ABSTRACT FROM AUTHOR]

Experimental data need to be assessed for purposes of model identification, estimation of model parameters and consequences of misspecified model fits. Here the first and third factors are considered via analytic formulations for the distribution of the maximum likelihood estimates. When estimating this distribution with statistics, it is a tradition to invert the roles of population quantities and quantities that have been estimated from the observed sample. If the model is known, simulations, normal approximations and p*-formula methods can be used. However, exact analytic methods for describing the estimator density are recommended. One of the methods (TED) can be used when the data generating model differs from the estimation model, which allows for the estimation of common parameters across a suite of candidate models. Information criteria such as AIC can be used to pick a winning model. AIC is however approximate and generally only asymptotically correct. For fairly simple models, where expressions remain tractable, the exact estimator density under TED allows for comparisons between models. This is illustrated via a novel information criterion. Three linear models are compared and fitted to econometric data on patent filings. [ABSTRACT FROM AUTHOR]

The spatio-temporal modelling and forecasting of incidences of crimes have now become a routine part of crime prevention operations. However, obtaining reliable forecasts for cases of changing spatial boundaries using models which take the influences of exogenous factors on the spatial and temporal dynamics of crime into account remains a challenge. The proposed Dynamic Spatial Distribution Approach (DSDA) is a modelling approach that provides spatio-temporal forecasts that incorporate the influences of salient weather conditions that have a bearing on crime dynamics at both the temporal and spatial levels. The DSDA starts with modelling and forecasting the dataset of the entire area of interest as a whole. Given reliable forecasts, the DSDA spatially disaggregates them by extrapolating the spatial patterns identified from the historic data. This is carried out by firstly identifying the spatial pattern and then defining a set of weights, one for each of the clusters making up this pattern. A number of methods to determining these weights, including a benchmark, univariate and causal approaches are proposed. The DSDA was developed within a GIS and classical statistics environment. Applied to the daily number of criminal damage incidences in the City of Cardiff, UK, the DSDA yielded a city-wide forecast error of 3.51 crimes per day. The spatial disaggregation using weights identified using Least Squares estimates of expected crime percentages in each cluster yielded an average of 1.1240 crimes per day per cluster. The model used incorporated the influences of weekdays and ambient conditions on the spatial distribution of crime. [ABSTRACT FROM AUTHOR]

This paper considers parameter estimation for nonlinear and non-Gaussian state-space models with correlation. We propose an asymptotic quasilikelihood (AQL) approach which utilises a nonparametric kernel estimator of the conditional variance covariances matrix St to replace the true St in the standard quasi-likelihood. The kernel estimation avoids the risk of potential miss-specification of St and thus make the parameter estimator more robust. This has been further verified by empirical studies carried out in this paper. [ABSTRACT FROM AUTHOR]

The problem of estimating the intensity process of a doubly stochastic Poisson process is analyzed. Using covariance information, a recursive linear minimum mean-square error estimate is designed. Moreover, an efficient procedure for the computation of its associated error covariance is shown. The proposed solution becomes an alternative approach to the Kalman filter which is applicable under the only structural assumption that the intensity process to be estimated has a finite-dimensional covariance function. [ABSTRACT FROM AUTHOR]

In this paper, we present an interesting filtering algorithm to perform accurate estimation in jump Markov nonlinear systems, in case of multi-target tracking. With this paper, we aim to contribute in solving the problem of model based body motion estimation by using data coming from visual sensors. The Interacting Multiple Model (IMM) algorithm is specially designed to track accurately targets whose state and/or measurement (assumed to be linear) models changes during motion transition. However, when these models are nonlinear, the IMM algorithm must be modified in order to guarantee an accurate track. In order to deal with this problem, the IMM algorithm was combined with the Unscented Kalman Filter (UKF) [6]. Even if the later algorithm proved its efficacy in nonlinear model case; it presents a serious drawback in case of non Gaussian noise. To deal with this problem we propose to substitute the UKF with the Particle Filter (PF). To overcome the problem of data association, we propose the use of the JPDA approach, [12]. To reduce the computational burden of the latter technique, we choose firstly the most likely feasible events by applying a Genetic Algorithm; finally the derived algorithm from the combination of the IMM-PF algorithm and the GA-JPDA approach is noted GA-JPDA-IMM-PF. [ABSTRACT FROM AUTHOR]

Positive stable laws have become a standard tool in modelling heavy tailed data in such diverse areas as finance, engineering and survival analysis. Due to the non-existence of closed-form expression for the corresponding densities, standard procedures for estimation of the parameters of positive stable distributions appear to be computationally expensive. In this note we show that the first two moments of negative order provide a straightforward estimation procedure, in which the solution of the resulting equations exists, and leads to unique moment estimates for the parameters involved. Simulations and application of this method on real data are also included. [ABSTRACT FROM AUTHOR]