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Models for option pricing based on empirical characteristic function of returns

Karol Binkowski, Andrzej Kozek (2010)

Banach Center Publications

The standard Merton-Black-Scholes formula for European Option pricing serves only as approximation to real values of options. More advanced extensions include applications of Lévy processes and are based on characteristic functions, which are more convenient to use than the corresponding probability distributions. We found one of the Lewis (2001) general theoretical formulae for option pricing based on characteristic functions particularly suitable for a statistical approach to option pricing. By...

Models for stochastic mortality

Jan Iwanik (2007)

Applicationes Mathematicae

This paper is an attempt to present and analyse stochastic mortality models. We propose a couple of continuous-time stochastic models that are natural generalizations of the Gompertz law in the sense that they reduce to the Gompertz function when the volatility parameter is zero. We provide a statistical analysis of the available demographic data to show that the models fit historical data well. Finally, we give some practical examples for the multidimensional models.

Models gràfics d'independència.

Josep Maria Durán Rúbies (1999)

Qüestiió

Los modelos gráficos de independencia son una herramienta del análisis multivariante que utiliza gráficos para representar modelos. En particular, los grafos de independencia resumen y clarifican las interacciones entre variables, interacciones no siempre fáciles de interpretar, especialmente cuando en ellas intervienen tres o más variables.En este trabajo se proporciona, en clave pedagógica, una introducción a la teoría de grafos de independencia, comenzando por las nociones de independencia necesarias...

Moderate deviations for the Durbin–Watson statistic related to the first-order autoregressive process

S. Valère Bitseki Penda, Hacène Djellout, Frédéric Proïa (2014)

ESAIM: Probability and Statistics

The purpose of this paper is to investigate moderate deviations for the Durbin–Watson statistic associated with the stable first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We first establish a moderate deviation principle for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise. It enables us to provide a moderate deviation...

Moderate deviations for two sample t-statistics

Hongyuan Cao (2007)

ESAIM: Probability and Statistics

Let X1,...,Xn1 be a random sample from a population with mean µ1 and variance σ 1 2 , and X1,...,Xn1 be a random sample from another population with mean µ2 and variance σ 2 2 independent of {Xi,1 ≤ i ≤ n1}. Consider the two sample t-statistic T = X ¯ - Y ¯ - ( μ 1 - μ 2 ) s 1 2 / n 1 + s 2 2 / n 2 . This paper shows that ln P(T ≥ x) ~ -x²/2 for any x := x(n1,n2) satisfying x → ∞, x = o(n1 + n2)1/2 as n1,n2 → ∞ provided 0 < c1 ≤ n1/n2 ≤ c2 < ∞. If, in addition, E|X1|3 < ∞, E|Y1|3 < ∞, then P ( T ≥ x ) 1 - Φ ( x ) → 1 holds uniformly in x ∈ (O,o((n1 + n2)1/6))

Modified minimax quadratic estimation of variance components

Viktor Witkovský (1998)

Kybernetika

The paper deals with modified minimax quadratic estimation of variance and covariance components under full ellipsoidal restrictions. Based on the, so called, linear approach to estimation variance components, i. e. considering useful local transformation of the original model, we can directly adopt the results from the linear theory. Under normality assumption we can can derive the explicit form of the estimator which is formally find to be the Kuks–Olman type estimator.

Modified power divergence estimators in normal models – simulation and comparative study

Iva Frýdlová, Igor Vajda, Václav Kůs (2012)

Kybernetika

Point estimators based on minimization of information-theoretic divergences between empirical and hypothetical distribution induce a problem when working with continuous families which are measure-theoretically orthogonal with the family of empirical distributions. In this case, the φ -divergence is always equal to its upper bound, and the minimum φ -divergence estimates are trivial. Broniatowski and Vajda [3] proposed several modifications of the minimum divergence rule to provide a solution to the...

Moment estimation methods for stationary spatial Cox processes - A comparison

Jiří Dvořák, Michaela Prokešová (2012)

Kybernetika

In the present paper we consider the problem of fitting parametric spatial Cox point process models. We concentrate on the moment estimation methods based on the second order characteristics of the point process in question. These methods represent a simulation-free faster-to-compute alternative to the computationally intense maximum likelihood estimation. We give an overview of the available methods, discuss their properties and applicability. Further we present results of a simulation study in...

Monotonicity of Bayes estimators

Piotr Bolesław Nowak (2013)

Applicationes Mathematicae

Let X=(X₁,..., Xₙ) be a sample from a distribution with density f(x;θ), θ ∈ Θ ⊂ ℝ. In this article the Bayesian estimation of the parameter θ is considered. We examine whether the Bayes estimators of θ are pointwise ordered when the prior distributions are partially ordered. Various cases of loss function are studied. A lower bound for the survival function of the normal distribution is obtained.

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