Conditional VaR estimation using Pearson’s type IV distribution

Bhattacharyya, Malay; Chaudhary, Abhishek; Yadav, Gaurav

doi:10.1016/j.ejor.2007.07.021

Cited by 33 publications

(14 citation statements)

References 35 publications

(32 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Zhu and Galbraith (2011) use a generalised asymmetric Student's in conjunction with a nonlinear GARCH model to predict expected shortfall on the returns of six stocks and the S&P 500. Bhattacharyya et al (2008) use a Pearson type IV distribution, which is a further generalisation of the GB2, in conjunction with a GARCH model for estimation of CVaR using 14 national equity indices. Although they find their results superior to using a normal-GARCH combination, the Pearson type IV failed some goodness of fit tests.…”

Section: Literature Reviewmentioning

confidence: 99%

“…It is clear that accurate computation of both CVaR and Rachev ratios depend in turn on accurate computation of value at risk itself. The effect of departures from a normal distribution on commonly used risk measures, such as value at risk or conditional value at risk (also called expected shortfall) have been considered by several operational researchers including Stoyanov et al (2013), Goh et al (2012), Natarajan et al (2008) and Bhattacharyya et al (2008). In addition there is a large finance literature covering these two risk measures.…”

Section: Portfolio Risk Management Under Generalised Multivariate Stumentioning

confidence: 99%

See 1 more Smart Citation

Using parametric classification trees for model selection with applications to financial risk management

Adcock

Meade

2017

European Journal of Operational Research

View full text Add to dashboard Cite

We describe two parametric classification tree methods, which allow formal selection of a member of a class of generalised distributions. In the paper we consider generalised Beta distributions for non-negative random variables and the generalised skew-Student distribution for random variables distributed on the real line. We introduce a class of symmetric generalised multivariate Student distributions, members of which may also be selected using the classification trees. We present two versions of the parametric classification tree: specific to general and general to specific. We apply the classification methods to daily returns on stocks from a selection of 15 major, mid-cap and emerging markets. The results show that the majority of return distributions follow Student’s t, but that a non-negligible minority follow a symmetric generalised Student distribution. We confirm a well-known stylised fact about skewness: it tends not to be persistent. By contrast, kurtosis is persistent. Using the symmetric generalised multivariate Student distribution, we present a risk management study based on efficient portfolios constructed from UKFTSE250 stocks and specifically concerned with the computation of value at risk. The case study demonstrates that the model selection procedures based on the classification trees lead to more accurate computation of VaR than those based on the normal distribution or on non-parametric approaches. The study also shows that the normal distribution may be used for VaR computations for larger portfolios when the holding period is longer

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Section: Portfolio Risk Management Under Generalised Multivariate Stumentioning

confidence: 99%

Using parametric classification trees for model selection with applications to financial risk management

Adcock

Meade

2017

European Journal of Operational Research

View full text Add to dashboard Cite

show abstract

“…, and ε t satisfies the condition in (8). Then, if there exists a c = 1 such that ε * t satisfies the condition in (8) (i.e., u(c) = 1 for some positive c = 1), the PQMLE can not be identified under (8). Thus, we need Assumption 4 to rule out this un-desirable situation.…”

Section: •2 the Pearson's Type IV Distributionmentioning

confidence: 99%

A New Pearson-Type QMLE for Conditionally Heteroscedastic Models

Zhu

2015

Journal of Business & Economic Statistics

View full text Add to dashboard Cite

This paper proposes a novel Pearson-type quasi maximum likelihood estimator (QMLE) of GARCH(p, q) models. Unlike the existing Gaussian QMLE, Laplacian QMLE, generalized non-Gaussian QMLE, or LAD estimator, our Pearsonian QMLE (PQMLE) captures not just the heavy-tailed but also the skewed innovations. Under strict stationarity and some weak moment conditions, the strong consistency and asymptotic normality of the PQMLE are obtained. With no further efforts, the PQMLE can be applied to other conditionally heteroskedastic models. A simulation study is carried out to assess the performance of the PQMLE. Two applications to four major stock indexes and two exchange rates further highlight the importance of our new method. Heavy-tailed and skewed innovations are often observed together in practice, and the PQMLE now gives us a systematical way to capture these two co-existing features.

show abstract

“…The last system of equations has been applied in financial time series by Bhattacharyya, Chaudhary, and Yadav (2008), Brännäs and Nordman (2003), and Premaratne and Bera (2005). Since the variable domain of the Pearson type-IV distribution is (−∞, + ∞), Chen and Nie (2008) proposed a lognormal sum approximation using a variant of the Pearson distribution to account for the (0, + ∞) domain.…”

Section: Introductionmentioning

confidence: 99%