On the Distributional Characterization of Daily Log‐Returns of a World Stock Index

Fergusson, Kevin; Platen, Eckhard

doi:10.1080/13504860500394052

Cited by 67 publications

(37 citation statements)

References 21 publications

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“…These parametric assumptions, however, may not always be appropriate, resulting in inaccurate estimates of the underlying density of the log returns (Fergusson and Platen, 2006).…”

Section: Sandp 500 Log Returns Data Setmentioning

confidence: 99%

“…General finance models assume that returns are normally distributed or follow some other popular unimodal parametric distribution (Fergusson and Platen, 2006). These parametric assumptions, however, may not always be appropriate, resulting in inaccurate estimates of the underlying density of the log returns (Fergusson and Platen, 2006).…”

Section: Sandp 500 Log Returns Data Setmentioning

confidence: 99%

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Unimodal density estimation using Bernstein polynomials

Turnbull

Ghosh

2014

Computational Statistics & Data Analysis

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The estimation of probability density functions is one of the fundamental aspects of any statistical inference. Many data analyses are based on an assumed family of parametric models, which are known to be unimodal (e.g., exponential family, etc.). Often a histogram suggests the unimodality of the underlying density function. Parametric assumptions, however, may not be adequate for many inferential problems. This paper presents a flexible class of mixture of Beta densities that are constrained to be unimodal. We show that the estimation of the mixing weights, and the number of mixing components, can be accomplished using a weighted least squares criteria subject to a set of linear inequality constraints. We efficiently compute the number of mixing components and associated mixing weights of the beta mixture using quadratic programming techniques. Three criterion for selecting the number of mixing weights are presented and compared in a small simulation study. More extensive simulation studies are conducted to demonstrate the performance of the density estimates in terms of popular functional norms (e.g., L p norms). The true underlying densities are allowed to be unimodal symmetric and skewed, with finite, infinite or semi-finite supports. Code for an R function is provided which allows the user to input a data set and returns the estimated density, distribution, quantile, and random sample generating functions.

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“…These parametric assumptions, however, may not always be appropriate, resulting in inaccurate estimates of the underlying density of the log returns (Fergusson and Platen, 2006).…”

Section: Sandp 500 Log Returns Data Setmentioning

confidence: 99%

Section: Sandp 500 Log Returns Data Setmentioning

confidence: 99%

Unimodal density estimation using Bernstein polynomials

Turnbull

Ghosh

2014

Computational Statistics & Data Analysis

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show abstract

“…That is, large deviations from the mean are more common than with the normal distribution, leading to a condition popularly known as "fat tails." For example, Fergusson and Platen (2006) find that a Student's t distribution with 4 degrees of freedom, which has fatter tails than the normal, fits data for stock index returns fairly accurately.…”

Section: A L and A L mentioning

confidence: 99%

Valuing guaranteed bank debt: The roles of the strength and size of the bank and the guarantor

Estrellaa

Schichb

2015

JEFS

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A contingent claims model of the value of sovereign guarantees of bank debt shows that the value decreases with the bank's own creditworthiness and increases with that of the sovereign as well as with bank and sovereign size. Using cross-sectional data for 188 large banks world-wide from 2007 to 2013, empirical results are consistent with the model's implications, suggesting that the implicit support for a bank is higher when the bank is larger, when the bank is weaker, and when the country in which the bank is headquartered is larger or more creditworthy. While bank-specific factors matter as well as those related to the sovereign of the country where the bank is located, the effect on the value of sovereign guarantees of changes in bank strength dominate those in sovereign strength.

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“…These are also given in [17] and are also now available on the Wikipedia page on quantile functions [16]. The case n = 4 is an interesting case as it is known exactly, in the boundary case where kurtosis is infinite, and there is some evidence from work by Fergusson and Platen [7] that it is a good case for modelling daily world index log-returns. We shall therefore develop this in some detail.…”

Section: Accuracy and Numerical Methodsmentioning

confidence: 99%

Quantile mechanics II: changes of variables in Monte Carlo methods and GPU-optimised normal quantiles

Shaw

Luu

Brickman³

2014

Eur. J. Appl. Math

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With financial modelling requiring a better understanding of model risk, it is helpful to be able to vary assumptions about underlying probability distributions in an efficient manner, preferably without the noise induced by resampling distributions managed by Monte Carlo methods. This article presents differential equations and solution methods for the functions of the form Q(x) = F −1 (G(x)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one distribution into samples from another. The method may be developed analytically for certain special cases, and illuminate the idea that it is a more precise form of the traditional Cornish-Fisher expansion. In this manner the model risk of distributional risk may be assessed free of the Monte Carlo noise associated with resampling. The method may also be regarded as providing both analytical and numerical bases for doing more precise Cornish-Fisher transformations. Examples are given of equations for converting normal samples to Student t, and converting exponential to hyperbolic, variance gamma and normal. In the case of the normal distribution, the change of variables employed allows the sampling to take place to good accuracy based on a single rational approximation over a very wide range of the sample space. The avoidance of any branching statement is of use in optimal GPU computations as it avoids the effect of warp divergence, and we give examples of branch-free normal quantiles that offer performance improvements in a GPU environment, while retaining the best precision characteristics of well-known methods. We also offer models based on a low-probability of warp divergence. Comparisons of new and old forms are made on the Nvidia Quadro 4000, GTX 285 and 480, and Tesla C2050 GPUs. We argue that in single-precision mode, the change-of-variables approach offers performance competitive with the fastest existing scheme while substantially improving precision, and that in double-precision mode, this approach offers the most GPU-optimal Gaussian quantile yet, and without compromise on precision for Monte Carlo applications, working twice as fast as the CUDA 4 library function with increased precision.

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On the Distributional Characterization of Daily Log‐Returns of a World Stock Index

Cited by 67 publications

References 21 publications

Unimodal density estimation using Bernstein polynomials

Unimodal density estimation using Bernstein polynomials

Valuing guaranteed bank debt: The roles of the strength and size of the bank and the guarantor

Quantile mechanics II: changes of variables in Monte Carlo methods and GPU-optimised normal quantiles

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