14 Probability distributions for financial models

McDonald, James B.

doi:10.1016/s0169-7161(96)14016-5

Cited by 190 publications

(174 citation statements)

References 59 publications

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“…As such, a test based onβ might be preferred, or a test based on the significance of the asymmetry parameter of another (flexible, fat-tailed, asymmetric) distribution. This is generally referred to as partially adaptive estimation, and is useful because it avoids some of the disadvantages of nonparametric inference; see, for example, McDonald (1991McDonald ( , 1997.…”

Section: Basic Analysismentioning

confidence: 99%

An econometric analysis of emission allowance prices

Paolella

Taschini

2008

Journal of Banking & Finance

303

138

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Knowledge of the statistical distribution of the prices of emission allowances, and their forecastability, are crucial in constructing, among other things, purchasing and risk management strategies in the emissions-constrained markets. This paper analyzes the two emission permits markets, CO2 in Europe, and SO2 in the US, and investigates a model for dealing with the unique stylized facts of this type of data. Its effectiveness in terms of model fit and out-of-sample value-at-risk-forecasting, as compared to models commonly used in risk-forecasting contexts, is demonstrated. An Econometric Analysis of Emission Trading Allowances November 2006Abstract World power and gas markets have a natural relationship with global tradable carbon permits markets, including the U.S. Clean Air Act Amendments and the EU Emissions Trading Scheme, the latter officially launched in January 2005. Electric utilities operate their power plants based in part on the price of the power and the relative cost of coal and natural gas. As both carbon dioxide and sulphur dioxide are by-products of the coal burning process, the new factors of SO 2 and CO 2 emissions allowances come into play in a carbon constrained economy. Now that a price has been put on such allowances, the differences in carbon intensity for coal and gas could potentially change the way companies run their power plants. Moreover, knowledge of the statistical distribution of emission trading allowances, and its forecastability, becomes crucial in constructing optimal hedging and purchasing strategies in the carbon market. This paper provides an in-depth analysis of available data addressing the unconditional tail behavior and the inherent heteroskedastic dynamics in the returns on the emissions allowances.Keywords: Environmental Finance, GARCH, Greenhouse Gases, Mixture Models, Tail Estimation. * Part of the research of the authors has been carried out within the National Centre of Competence in Research "Financial Valuation and Risk Management" (NCCR FINRISK), which is a research program supported by the Swiss National Science Foundation. Corresponding author: taschini@isb.unizh.ch.† The help from Enviros Climate Change Group as well as the data base on sulfur dioxide spot prices from the Chicago Climate Exchange are gratefully acknowledged. The authors would like to thank Pauline Barrieu, Marc Chesney, George Daskalakis, Helyette Geman, Daniel Giamouridis, Rajna Gibson, Wolfgang Härdle, Gikas Hardouvelis, Raphael Markellos, Nikitas Pittis, Dimitris Psychoyios, Costas Vorlow, and Alexander Wagner for their helpful discussions and comments. We wish to also thank Sven-C. Steude for the programming assistance on the mixed normal models used in the paper.

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Section: Basic Analysismentioning

confidence: 99%

An econometric analysis of emission allowance prices

Paolella

Taschini

2008

Journal of Banking & Finance

303

138

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“…The GB2, like the g-and-h distribution, can accommodate a wide variety of tail-thicknesses and permits skew-18 ness as well. Many of the important properties and applications of the GB2 distribution can be found in McDonald (1996) and McDonald and Xu (1995). Bookstabber and McDonald (1987) and Dutta and Babbel (2005) have explored the possibility of modeling equity and interest rates respectively using GB2.…”

Section: The Gb2 Distributionmentioning

confidence: 99%

A Tale of Tails: An Empirical Analysis of Loss Distribution Models for Estimating Operational Risk Capital

2006

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“…In other words, an insurance company may bring its risk to minimum by choosing the x q above to be the deductible in a policy with a deductible, or the retention level in the context of reinsurance contracts. Bian and Tiku (1997) and MacDonald (1996) suggest putting k p = (2p -3)/2 if p > 3/2 to obtain the so-called Generalized Student-t (GST) univariate distribution with density (4.13)…”

Section: G) Under Condition (37) the Tail Variance Of X Is Given Bymentioning

confidence: 99%

Tail Variance Premium with Applications for Elliptical Portfolio of Risks

Furman¹,

Landsman²

2006

ASTIN Bull.

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In this paper we consider the important circumstances involved when risk managers are concerned with risks that exceed a certain threshold. Such conditions are well-known to insurance professionals, for instance in the context of policies involving deductibles and reinsurance contracts. We propose a new premium called tail variance premium (TVP) which answers the demands of these circumstances. In addition, we suggest a number of risk measures associated with TVP. While the well-known tail conditional expectation risk measure provides a risk manager with information about the average of the tail of the loss distribution, tail variance risk measure (TV) estimates the variability along such a tail. Furthermore, given a multivariate setup, we offer a number of allocation techniques which preserve different desirable properties (sub-additivity and fulladditivity, for instance). We are able to derive explicit expressions for TV and TVP, and risk capital decomposition rules based on them, in the general framework of multivariate elliptical distributions. This class is very popular among actuaries and risk managers because it contains distributions with marginals whose tails are heavier than those of normal distributions. This distinctive feature is desirable when modeling financial datasets. Moreover, according to our results, in some cases there exists an optimal threshold, such that by choosing it, an insurance company minimizes its risk.

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14 Probability distributions for financial models

Cited by 190 publications

References 59 publications

An econometric analysis of emission allowance prices

An econometric analysis of emission allowance prices

A Tale of Tails: An Empirical Analysis of Loss Distribution Models for Estimating Operational Risk Capital

Tail Variance Premium with Applications for Elliptical Portfolio of Risks

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